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The disjoint properties of finitely many composition operators acting on the weighted Banach spaces of holomorphic functions in the unit disk were investigated in this paper.

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.

Analyzing large prehistoric rock avalanches provides significant data for evaluating the disaster posed by these relatively infrequent but destructive geological events. This paper attempts to study the characteristics and dynamics of the Ganqiuchi granitic rock avalanche, in the middle of the northern margin of Qinling Mountains, 30 km to the south of Xi’an, Shaanxi Province, China. In plane view, this rock avalanche is characterized by source area, accumulation area and dammed lake area. Based on previous studies, historical records and regional geological data, the major trigger of the Ganqiuchi rock avalanche is considered to be a strong paleo-earthquake with tremendous energy. The in situ deposit block size distributions of the intact rock mass and the debris deposits are presented and analyzed by using a simple model for estimating the number of fragmentation cycles that the blocks underwent. The results show that the primary controlling factor of the fragmentation process is the pre-existing fractures, and there is a relationship between the potential energy and the fragmentation energy: the latter is approximately 20% of the former. Based on the dynamic discrete element technique, the study proposes a four-stage model for the dynamic course of the Ganqiuchi rock avalanche: (1) failing; (2) highspeed sliding; (3) collision with obstacles; (4) decelerated sliding, which has implication for hazard assessment of the potential rock avalanches in China and other countries with similar geological setting.

This paper identifies a class of complex symmetric weighted composition operators on H2(D) that includes both the unitary and the Hermitian weighted composition operators, as well as a class of normal weighted composition operators identified by Bourdon and Narayan. A characterization of algebraic weighted composition operators with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional.

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

In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.

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 present the new characterizations, in terms of the sequence $$\{z^j\}_{j=1}^\infty $$, about the boundedness and essential norm estimation for the products of differentiation and composition operators from logarithmic Bloch spaces to $$\mu $$-Bloch spaces on the unit disk. Then our main results are applied to show the boundedness of a non-trivial product operator $$C_\varphi D^m$$ with $$\varphi (z)=z^2$$.

Let G be a locally compact second countable Hausdorff space with a positive regular Borel measure λ, where λ is invariant under a continuous injective mapping φ : G → G. We characterize the disjoint hypercyclicity of finite weighted translations generated by φ acting on the weighted space Lp (G, ω) (1 ≤ p < ∞).

Let $$S^p$$ be the space of holomorphic functions whose derivative lies in the classical Hardy space $$H^p$$ over the unit disk. We prove in this paper that the composition operator $$C_\varphi $$ with $$\varphi $$ an automorphism is hypercyclic on $$S^p$$ , $$0

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.

In this article, we provide a complete description of the spectra of linear fractional composition operators acting on the growth space and Bloch space over the upper half-plane. In addition, we also prove that the norm, essential norm, spectral radius and essential spectral radius of a composition operator acting on the growth space are all equal.

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 .

In this article, we characterize the disjoint hypercyclicity of finite weighted pseudo-shifts on an arbitrary Banach sequence space. Moreover, we obtain some interesting consequences of this characterization.

In this paper, we characterize disjoint hypercyclic powers of weighted pseudo-shifts on an arbitrary F-sequence space. As a special case, we deduce the equivalent conditions for the disjoint hypercyclicity of finitely many different powers of weighted shifts on \(\ell ^2({\mathbb {Z},\mathcal {K}})\) with weight sequence \(\{A_n\}_{n=-\infty }^{\infty }\) of positive invertible diagonal operators on \(\mathcal {K}\).

In this paper, we completely characterize the finite rank commutator and semicommutator of two monomial-type Toeplitz operators on the weighted Bergman space or on the weighted pluriharmonic Bergman space of the unit polydisk. As a consequence, some interesting new phenomenons appear in operator theory on the unit polydisk which are different from that on the unit disk and the unit ball.

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.

Density functional theory (DFT) calculations were performed to investigate oxygen adsorption on Mo2C(001) and (201)surfaces at different coverage. The energies and structures of oxygen from lowest to saturated coverages were clearly identified on each surface. Thermodynamics method was introduced to reveal the roles of temperature, pressure as well as oxygen sources (O2, H2O and CO2) on the surface oxygen coverage, which is related to the surface oxidation. On the basis of phase diagram, we can easily identify the stable oxygen coverage at different defined conditions. In addition, it reveals that O2 is the strongest oxidant, which results in the full coverage of oxygen on both surfaces in a wide range of temperature and pressure. Then, H2O and CO2 are weaker oxidants, which could only cause partial oxidation of Mo2C surfaces. These results indicate the facile oxidation of Mo2C catalyst. The possible ways to avoid surface oxidation are keeping higher temperature and H2 pressure in the gas phase.

We give some simple norm estimates of the difference of weighted composition operators acting from Lipschitz space $$\mathcal {L}_\alpha $$ to the space $$H^\infty $$ of all analytic functions on the unit disk, and showing that any two bounded weighted composition operators are pathwise connected. We also obtain some necessary or sufficient conditions for the difference to be compact. Unlike the equivalence of the boundedness and compactness for weighted composition operators from $$\mathcal {L}_\alpha $$ to $$H^\infty ,$$ we show that there exists a difference which is bounded, but not compact.

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.

We use a generalised Nevanlinna counting function to compute the Hilbert–Schmidt norm of a composition operator on the Bergman space $L_{a}^{2}(\mathbb{D})$ and weighted Bergman spaces $L_{a}^{1}(\text{d}A_{\unicode[STIX]{x1D6FC}})$ when $\unicode[STIX]{x1D6FC}$ is a nonnegative integer.

We characterize the boundedness and compactness of the differences of weighted differentiation composition operators $$ {D}_{\varphi_1,{u}_1}^n-{D}_{\varphi_2,{u}_2}^n, $$ where n ∈ ℕ0, u1,u2 ∈ H( $$ \mathbb{D} $$ ), and $$ \varphi $$ 1, $$ \varphi $$ 2 2 S( $$ \mathbb{D} $$ ), from mixed-norm spaces H(p, q, ϕ), where 0 < p, q < ∞ and ϕ is normal, to weighted-type spaces H ∞ .

Let $$\varphi $$ be a complex-valued function in the plane $${\mathbb {C}}.$$ The superposition operator is defined by $$ S_\varphi (f)=\varphi \circ f$$ . In this paper, we characterize the nonlinear superposition operators $$S_\varphi $$ acting between the Zygmund-type and Bloch-type spaces in terms of the order and type or the degree of $$\varphi $$ .

In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch-type spaces and calculate its essential norm in terms of the n-th power of induced analytic self-map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.

The authors characterize the order boundedness of weighted composition operators acting between Dirichlet type spaces.

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 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.

For an analytic self-map of the unit disk in the complex plane and a nonnegative integer , the composition operator followed by differentiation on is defined byfor and . In this paper, we study the boundedness and compactness of from or spaces to Bloch-type spaces or little Bloch-type spaces.

In this paper, analogues of the Berkson–Porta formula for the infinitesimal generators of one-parameter semigroup of holomorphic self-maps on the polydisk are obtained. We give a necessary and sufficient condition for a holomorphic vector field to be an infinitesimal generator which improves the theorem given by Contreras, de Fabritiis and Diaz-Madrigal.

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.

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.

We study the ranks of commutators and generalized semicommutators of Toeplitz operators with quasihomogeneous symbols on both the harmonic Bergman space and the Bergman Space. In particular, when one of quasihomogeneous symbols is the the form of $e^{ik\theta }r^{m}$, we first obtain specific sufficient and necessary conditions for commutators and generalized semicommutators to be finite rank. Then we make further efforts to determine the range of each finite rank commutator and generalized semicommutators, and consequently the explicit canonical form and the rank are obtained. Thus, the finite rank problem of commutators and generalized semicommutators of such special Toeplitz operators is completely solved. As applications, several interesting corollaries and nontrivial examples are given. Also, we show close connections of the finite rank problem between the harmonic Bergman space and Bergman space cases., Comment: 29 pages