We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators on the harmonic Bergman space is equal to a Toeplitz operator , then the product is also the Toeplitz operator , and hence commutes with . From this we give necessary and sufficient conditions for the product of two Toeplitz operators, one quasihomogeneous and the other monomial, to be a Toeplitz operator.
The chaos of the differentiation operator on generalized weighted Bergman spaces of entire functions has been characterized recently by Bonet and Bonilla in [CAOT 2013], when the differentiation operator is continuous. Motivated by those, we investigate conditions to ensure that finite many powers of differentiation operators are disjoint hypercyclic on generalized weighted Bergman spaces of entire functions.
Let and be holomorphic self-maps of the unit disk, and denote by , the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.
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 , 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. Lindström and E. Wolf: Essential norm of the difference of weighted composition operators....
Let be a holomorphic function and a holomorphic self-map of the open unit disk in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators from Zygmund type spaces to Bloch type spaces in in terms of , , their derivatives, and , the -th power of . Moreover, we obtain some similar estimates for the essential norms of the operators , from which sufficient and necessary conditions of compactness of follows immediately.
We investigate isometric composition operators on the weighted Dirichlet space with standard weights , . The main technique used comes from Martín and Vukotić who completely characterized the isometric composition operators on the classical Dirichlet space . We solve some of these but not in general. We also investigate the situation when is equipped with another equivalent norm.
Let be a complex Banach space, with the unit ball . We study the spectrum of a bounded weighted composition operator on determined by an analytic symbol with a fixed point in such that is a relatively compact subset of , where is an analytic function on .
This paper characterizes the boundedness and compactness of weighted composition operators between a weighted-type space and the Hardy space on the unit ball of ℂⁿ.
Let H() denote the space of all holomorphic functions on the unit ball ⊂ ℂⁿ. Let φ be a holomorphic self-map of and u∈ H(). The weighted composition operator on H() is defined by . We investigate the boundedness and compactness of induced by u and φ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.
This paper identifies a class of complex symmetric weighted composition operators on 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.
Let be a locally compact group and let 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 in terms of the weights. Sufficient and...
Page 1