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In this paper, we characterize the boundedness and compactness for weighted composition operators on the Fock-Sobolev space F p,m(Cn), 0 < p < ∞. We prove that no nontrivial unitary or self-adjoint weighted composition operators exist on F2,m(Cn) when m ≥ 1. As an application, we also prove that there exist only trivial J -symmetric weighted composition operators on F2,m(Cn) when m ≥ 1. [ABSTRACT FROM AUTHOR]

We study how certain Volterra type operators compactly intertwine with composition operators on the space of bounded analytic functions and composition operators on the Bloch space of the unit disk. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space H²(BN) and weighted Bergman spaces Aa²(BN), where BN is the unit ball of the N-dimensional complex space. By taking N = 1, BN = D the unit disc, we also complete the discussion about the spectrum of a weighted composition operator when it is invertible on H²(D) or A²(D). [ABSTRACT FROM AUTHOR]

We characterize the disjoint supercyclicity of finitely many different powers of weighted shifts acting on the weighted sequence spaces l²(...,w), c0(...,w), and l²(Z,w), c0(...,w), where w = (w1)1 is a positive weight sequence satisfying w1 ≥ 1 for every i ∈ ... (or i ∈ ...). [ABSTRACT FROM AUTHOR]

We characterize the boundedness and compactness of differences of the composition operators followed by differentiation between weighted Banach spaces of holomorphic functions in the unit disk. As their corollaries, some related results on the differences of composition operators acting from weighted Banach spaces to weighted Bloch type spaces are also obtained. [ABSTRACT FROM AUTHOR]

This paper characterizes the boundedness and compactness of the product of extended Cesàro operator and composition operator from Lipschitz space to F(p,q,s) space on the unit ball of ℁n. [ABSTRACT FROM AUTHOR]

For φ a holomorphic self-map of the unit ball BN of ℂN, and u ∈ H∞(BN) (the Banach space of bounded holomorphic functions on BN), we investigate the essential norm and spectrum of the weighted composition operator uCφ acting on the space H∞(BN). For φ univalent, not unitary on any slice, and fixing a point of BN, we obtain a complete characterization of the spectrum of uCφ. [ABSTRACT FROM AUTHOR]

We investigate the composition operators Cφ acting on the Bergman space of the unit disc D, where φ is a holomorphic self-map of D. Some new conditions for Cφ to belong to the Schatten class Sp are obtained. We also construct a compact composition operator which does not belong to any Schatten class. [ABSTRACT FROM AUTHOR]

Let Bn be the unit ball of Cn and φ = (φ1, . . . , φn) a holomorphic self-map of Bn. Let 0 < p,s < ∞, −n−1 < q < ∞, q s > −1,α > 0, and let Cφ be the composition operator between the space F(p, q, s) and α-Bloch space Bα induced by φ. This paper gives an estimate of the essential norm of Cφ. As a consequence, a necessary and sufficient condition for the composition operator Cφ to be compact from F(p, q, s) to Bα is obtained. [ABSTRACT FROM AUTHOR]

We characterize the isometries on the products of composition and integral operators on the Bloch type space in the disk. [ABSTRACT FROM AUTHOR]

In this paper, we first discuss some basic results concerning Toeplitz operators with quasihomogeneous symbols (i.e., symbols being of the form $ e^{iptheta }varphi $, where $varphi $ is a radial function) on the harmonic Bergman space. Then we determine when the product of two Toeplitz operators with quasihomogeneous symbols is a Toeplitz operator. [ABSTRACT FROM AUTHOR]

Let φ and ψ be holomorphic self-maps of the unit polydisc Un in the n-dimensional complex space, and denote by Cφ and Cψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators Cφ - Cψ from Bloch space to bounded holomorphic function space in the unit polydisc. The compactness of the difference is also characterized. [ABSTRACT FROM AUTHOR]

This paper gives some estimates of the essential norm for the difference of composition operators induced by φ and φ acting on the space, H∞(Dn), of bounded analytic functions on the unit polydisc DE;n, where φ and φ are holomorphic self-maps of Dn. As a consequence, one obtains conditions in terms of the Carathéodory distance on Dn that characterizes those pairs of holomorphic self-maps of the polydisc for which the difference of two composition operators on H∞(Dn) is compact. [ABSTRACT FROM AUTHOR]

The article reports on the study of the spectrum structure of compact operators on Hardy spaces of a unit ball. It aims to determine the spectrum of compact operators in weighted hardy spaces of a unit ball through eigenvalues of the compact operators. It uses differential equations and different theorems of inequalities in analyzing the spectrum structure. It also shows that the spectral radius of compact operators are nonautomorphism linear fractional map which takes the unit sphere to an ellipsoid sphere.