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The spectrum of a weighted composition operator $$C_{\psi , \varphi }$$ that is induced by an automorphism has been investigated for over 50 years. However, many results are got only under the condition that the weight function $$\psi $$ is continuous up to the boundary. In this paper we study the spectra and essential spectra of $$C_{\psi ,\varphi }$$ on weighted Bergman spaces when $$\varphi $$ is an elliptic automorphism, without the assumption that $$\psi $$ is continuous up to the boundary.

Recently, significant effort has been made toward the development of graphene-based visible-ligh-responsive photocatalysts and their application to dye wastewater treatment. Herein, a series of octahedral ZnFe2O4/graphene (ZnFe2O4-G) nanocomposites were synthesized using a one-pot solvothermal reaction without the need of a surfactant as novel bifunctional materials exhibiting both high adsorption and good visible-light-responsive photocatalyst properties. The crystal structure, morphology and photocatalytic degradation properties, as well as adsorption behavior, of the octahedral ZnFe2O4/graphene composites were investigated in detail. The adsorption capacity and UV–vis spectrometry results indicate that the dye removal efficiency over the samples followed the order of: methylene blue (MB) > rhodamine B (RhB) > methyl orange (MO). The ZnFe2O4-G materials exhited enhanced photocatalytic degradation properties for cationic dyes (MB and RhB) compared to those for the anionic dye (MO). In addition, the experimental results indicate that the ZnFe2O4-G materials can decompose H2O2 in the visible-light photocatalytic process to form hydroxyl radicals (•OH), which are mainly responsible for the photodegradation of the organic contaminants.

We characterize the hypercyclicity of weighted composition operators on the weighted little Bloch space B 0 α , α > 0 .

In this paper, we discussed the equivalent conditions for the boundedness and compactness of several Volterra-type operators acting from general F(p,q,s) space to Bloch-Orlicz and Zygmund-Orlicz spaces.

In this paper, we show that for $$T\in B({\mathcal {H}})$$ , if $${\mathcal {M}}$$ is almost-invariant for T, then every maximal almost-invariant subspace of $${\mathcal {M}}$$ is of codimension 1 in $${\mathcal {M}}$$ , where $${\mathcal {H}}$$ is a separable, infinite-dimensional Hilbert space. We also describe the maximal hyperinvariant subspaces for normal operators with all the dimensions of eigenspaces at most 1 acting on $${\mathcal {H}}$$ . Our result is that for each hyperinvariant subspace, all its maximal hyperinvariant subspaces are also of codimension 1 in it.

In this paper, we completely characterize the finite rank commutator and semi-commutator of two monomial-type Toeplitz operators on the Bergman space of certain weakly pseudoconvex domains. Somewhat surprisingly, there are not only plenty of commuting monomial-type Toeplitz operators but also non-trivial semi-commuting monomial-type Toeplitz operators. Our results are new even for the unit ball.

This paper characterizes the boundedness and compactness of the differences of weighted differentiation composition operators acting from the ?-Bloch space B? to the space H? of bounded holomorphic functions on the unit disk D.

Let $I$ be a countably infinite index set, and let $X$ be a Banach sequence space over $I$ . In this article, we characterize the disjoint hypercyclic and supercyclic weighted pseudoshift operators on $X$ in terms of the weights, the OP-basis, and the shift mappings on $I$ . Also, the shifts on weighted $L^{p}$ spaces of a directed tree and the operator weighted shifts on $\ell ^{2}(\mathbb{Z},\mathcal{K})$ are investigated as special cases.

Let S ( D ) be the collection of all holomorphic self-maps on D of the complex plane C , and C φ the composition operator induced by φ ∈ S ( D ) . We obtain that there are no hypercyclic composition operators on the little Bloch space B 0 and the Besov space B p .

Let G be a locally compact group and let 1 ≤ p < 1. Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space L p(G) in terms of the weights. Sufficient and necessary conditions for disjoint hypercyclic and disjoint supercyclic powers of weighted translations generated by aperiodic elements on groups will be given.

The structures and energies of the B and Ga incorporated γ-alumina surface as well as the adsorption of water are investigated using dispersion corrected density functional theory. The results show that the substitution of surface Al atom by B atom is not so favored as Ga atom. The substitution reaction prefers to occur at the tricoordinated A(4) sites. However, the substitution reaction becomes less thermodynamically favored when more Al atoms are substituted by B and Ga atoms on the surface. Moreover, the substitution of bulk Al atoms is not so favored as the Al atoms by B and Ga on the surface. The γ-alumina surface is found to have stronger adsorption ability for water than the B and Ga incorporated surface. The total adsorption energy increases as water coverage increases, while the stepwise adsorption energy decreases. The studies show the coverage of water at 7.5 H2O/nm2 (five H2O molecules per unit cell) can fully cover the active sites and the further water molecule could only be physically adsorbed on the surface.

In this article, we investigate the mean ergodicity of composition operators acting on the Hardy space $$H^p({\mathbb {D}})$$ , $$1\le p

In this article, we first give an essential characterization of Toeplitz operators with quasihomogeneous symbols on the weighted pluriharmonic Bergman space of the unit polydisk. Then we completely characterize when the product of two Toeplitz operators with monomial-type symbols is a Toeplitz operator. As a result, some interesting higher-dimensional phenomena appear on the unit polydisk.

We investigate isometric composition operators on the weighted Dirichlet space \({D_\alpha }\) with standard weights \({(1 - {\left| z \right|^2})^\alpha },\alpha > - 1\). The main technique used comes from Martin and Vukotic who completely characterized the isometric composition operators on the classical Dirichlet space D. We solve some of these but not in general. We also investigate the situation when \({D_\alpha }\) is equipped with another equivalent norm.

We discuss the frequent hypercyclicity and hypercyclicity of multiples of the linear fractional composition operators on A α p and give equivalent conditions of the frequent hypercyclicity and hypercyclicity. We also characterize disjoint hypercyclicity and disjoint mixing behavior of finitely many linear fractional composition operators on the weighted Bergman spaces A α p .

In the present paper, we investigate the disjoint mixing property of finitely many linear fractional composition operators acting on the space of holomorphic functions on the unit ball in C N , and generalize parts of the results obtained by Bes, Martin and Peris in 2011.

In this paper, we investigate when weighted composition operators acting on Dirichlet spaces $\mathcal{D}(\mathbb{B}_{N})$ are complex symmetric with respect to some special conjugations, and provide some characterizations of Hermitian weighted composition operators on $\mathcal{D}(\mathbb{B}_{N})$. Furthermore, we give a sufficient and necessary condition for $J$-symmetric weighted composition operators on Hardy spaces $H^2(\mathbb{B}_{N})$ to be unitary or Hermitian, then some new examples of complex symmetric weighted composition operators on $H^2(\mathbb{B}_{N})$ are obtained. We also discuss the normality of complex symmetric weighted composition operators on $H^2(\mathbb{B}_{N})$., 18 pages

In this article, we give equivalent conditions for the hypercyclicity of bilateral operator-weighted shifts on $L^{2}(\mathcal{K})$ with weight sequence $\{A_{n}\}_{n=-\infty}^{\infty}$ of positive invertible diagonal operators on a separable complex Hilbert space $\mathcal{K}$ , as well as for hereditarily hypercyclicity and supercyclicity.

Flower-like and roughly spherical ZnO nanocrystalline have been successfully synthesized through mild wet chemical method. The photocatalytic activities of the prepared photocatalysts were evaluated by degradation of rhodamine B (RhB) and phenol under UV light irradiation. Remarkably, the roughly spherical ZnO powder via homogeneous precipitation method exhibited superior photocatalytic performance and better photo-stability than that of flower-like ZnO substrate by hydrothermal synthesis way. The enhanced photocatalytic properties could be attributed to more active catalytic sites and superior charges separation efficiency.

We characterize the supercyclic behavior of sequences of operators in a $C_0$-semigroup whose index set is a sector $\Delta$ in the complex plane $\mathbb{C}$.

Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk $$\mathbb{D}$$ in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators uC φ from Zygmund type spaces to Bloch type spaces in $$\mathbb{D}$$ in terms of u, φ, their derivatives, and φ n , the n-th power of φ. Moreover, we obtain some similar estimates for the essential norms of the operators uC φ , from which sufficient and necessary conditions of compactness of uC φ follows immediately.

In this paper we show that the property of disjoint supercyclic operators T1, ⋯, TN satisfying d-supercyclicity criterion on the same Hilbert space is equivalent to disjointness in supercyclicity of the corresponding left multiplication operators induced by T1, ⋯, TN in the strong operator topology. Besides, by the similar discussion, we also obtain that d-hypercyclicity criterion for any T1, ⋯, TN on the same Hilbert space is equivalent to d-hypercyclicity of the corresponding left multiplication operators induced by T1, ⋯, TN in the ‖.‖2 topology.

We characterize the difference of derivative weighted composition operators on the Bergman space in the unit disk and determine when linear-fractional derivative weighted composition operators belong to the same component of the space of derivative weighted composition operators on the Bergman space under the operator norm topology.

A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic for a nonzero subspace $M$ if $orb\left( {T,x} \right) \cap M$ is dense in $M$ for a vector $x \in X$, where $orb (T,x)=\{T^nx: n=0,1,2,\cdots\}$. Similarly, the bounded linear operator $T$ on a Banach space $X$ is called subspace-supercyclic for a nonzero subspace $M$ if there exists a vector whose projective orbit intersects the subspace $M$ in a relatively dense set. In this paper we provide a Subspace-Supercyclicity Criterion and offer two equivalent conditions of this criterion. At the same time, we also characterize other properties of subspace-supercyclic operators.

We give some new characterizations for compactness of weighted composition operators uCφ acting on Bloch-type spaces in terms of the power of the components of φ where φ is a holomorphic self-map of the polydisk 𝔻n, thus generalizing the results obtained by Hyvärinen and Lindström in 2012.

In this paper, we give a sufficient condition for the existence of a common universal subspace for various countable families of universal sequences of linear operators. Besides, we show that if σ p ( T ⁎ ) = ∅ , the unitary orbit of the supercyclic operator T contains a path of operators whose closure contains the entire unitary orbit with the strong operator topology, and yet every nonzero vector in the linear span of the orbit of a given supercyclic vector is a common supercyclic vector for the entire path.

We characterize disjoint mixing and disjoint hypercyclicity of finite many composition operators acting on the Hardy space on the unit ball.

【In this paper we first characterize the hereditarily hypercyclicity of the unilateral (or bilateral) weighted shifts on the spaces $L^2(\mathbb{N},\mathcal{K})$ (or $L^2(\mathbb{Z},\mathcal{K})$ ) with weight sequence { $A_n$ } of positive invertible diagonal operators on a separable complex Hilbert space $\mathcal{K}$ . Then we give the necessary and sufficient conditions for the supercyclicity of those weighted shifts, which extends some previous results of H. Salas. At last, we give some conditions for the supercyclicity of three different weighted shifts.】

We study the compact intertwining relations for compositionoperators, whose intertwining operators are Volterra type operators fromthe weighted Bergman spaces to the weighted Bloch spaces in the unitdisk. As consequences, we find a new connection between the weightedBergman spaces and little weighted Bloch spaces through this relations. 1. IntroductionIf X and Y are two Banach spaces, the symbol B(X,Y ) denotes the col-lection of all bounded linear operators from X to Y . Let K(X,Y ) be thecollection of all compact elements of B(X,Y ), and Q(X,Y) be the quotientset B(X,Y )/K(X,Y ).For linear operators A ∈ B(X,X), B ∈ B(Y,Y ) and T ∈ B(X,Y ), thephrase “T intertwines A and B in Q(X,Y)” (or “T intertwines A and B com-pactly”) means that(1.1) TA = BT mod K(X,Y ) with T 6= 0 .Notation A ∝ K B (T) represents the relation in equation (1.1). In fact, if T isan invertible operator on X, then the relation ∝ K is symmetric.We denote the class of all holomorphic functions on the complex unit disk Dby H(D), and the collection of all the holomorphic self mappings of Dby S(D).Let α > −1, 0 0. These settingsof α,β,γ and p are valid in the following context unless specifications.

The same scene, the infrared image and visible image fusion can concurrently take advantage of the original image information can overcome the limitations and differences of a single sensor image in terms of geometric, spectral and spatial resolution, to improve the quality of the image , which help to locate, identify and explain the physical phenomena and events. Put forward a kind of image fusion method based on wavelet transform. And for the wavelet decomposition of the frequency domain, respectively, discussed the principles of select high-frequency coefficients and low frequency coefficients, highlight the contours of parts and the weakening of the details section, fusion, image fusion has the characteristics of two or multiple images, more people or the visual characteristics of the machine, the image for further analysis and understanding, detection and identification or tracking of the target image.

In this paper, we study the boundness and compactness of differences of weighted composition operators from the Bloch space B to the space H ∞ of bounded analytic functions on the open unit ball of C n . Moreover, we estimate the norm and the essential norm of differences of composition operators from B to H ∞ .

Let $\varphi,\psi$ be the analytic self-maps of the unit ball ${\mathbb B}$, we characterize the Hilbert-Schmidt differences of two composition operator $C_\varphi$ and $C_\psi$ on weighted Bergman space $A_\alpha^2$, and give some conclusions about the topological structure of $\mathcal{C}(A_\alpha^2)$, the space of all bounded composition operators on $A_\alpha^2$ endowed with operator norm.

Some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(C_{\omega_1,\varphi_1}^* , C_{\omega_2,\varphi_2}^*)$ on the Hilbert space $\mathcal{H}$ of analytic functions is disk-cyclic (or codisk-cyclic) were investigated.

In this paper, we limit our analysis to the difference of the weighted composition operators acting from the Hardy space to weighted-type space in the unit ball of ℂN, and give some necessary and sufficient conditions for their boundedness or compactness. The results generalize the corresponding results on the single weighted composition operators and on the differences of composition operators, for example, M. Lindstrom and E. Wolf: Essential norm of the difference of weighted composition operators. Monatsh. Math. 153 (2008), 133–143.

Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spaces Bω and Bω,0 to mixed-norm space H(p,q,φ) on the unit ball B .

This paper discusses the hypercyclicity of weighted composi- tion operators acting on the space of holomorphic functions on the open unit ball BN of CN. Several analytic properties of linear fractional self- maps of BN are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.