Search

In this article, we give equivalent conditions for the hypercyclicity of bilateral operator-weighted shifts on L²(K) with weight sequence {An}n∞ =-∞ of positive invertible diagonal operators on a separable complex Hilbert space K, as well as for hereditarily hypercyclicity and supercyclicity. [ABSTRACT FROM AUTHOR]

A bounded linear operator T on a Banach space X is called subspace-hypercyclic for a nonzero subspace M if orb (T, x) ∩ M is dense in M for a vector x ∊ X, where orb(T, x) = {Tnx : n = 0, 1, 2, ... }. 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 subspacesupercyclic operators. [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]

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]

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]

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.

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. [ABSTRACT FROM AUTHOR]