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2. Disjoint hypercyclic powers of weighted translations on groups
- Creator:
- Zhang, Liang, Lu, Hui-Qiang, Fu, Xiao-Mei, and Zhou, Ze-Hua
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, disjoint hypercyclic powers of weighted translations, aperiodic element, locally compact group, 13, and 51
- Language:
- English
- Description:
- Let $G$ be a locally compact group and let $1 \le p < \infty.$ 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., Liang Zhang, Hui-Qiang Lu, Xiao-Mei Fu, Ze-Hua Zhou., and Obsahuje bibliografické odkazy
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
3. Essential norm of the difference of composition operators on Bloch space
- Creator:
- Yang, Ke-Ben and Zhou, Ze-Hua
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- {\it Bloch} space, composition operator, essential norm, difference, and compactness
- Language:
- English
- Description:
- Let $\varphi $ and $\psi $ be holomorphic self-maps of the unit disk, and denote by $C_\varphi $, $C_\psi $ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators $C_\varphi -C_\psi $ from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
4. Isometric composition operators on weighted Dirichlet space
- Creator:
- Han, Shi-An and Zhou, Ze-Hua
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, Dirichletova úloha, mathematics, Dirichlet problem, composition operator, weighted Dirichlet space, isometry, 13, and 51
- Language:
- English
- Description:
- 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 Martín and Vukotić 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., Shi-An Han, Ze-Hua Zhou., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
5. New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces
- Creator:
- Guo, Xin-Cui and Zhou, Ze-Hua
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, weighted composition operator, Zygmund type space, Bloch type space, essential norm, 13, and 51
- Language:
- English
- Description:
- Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk D in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators uCφ from Zygmund type spaces to Bloch type spaces in D in terms of u, φ, their derivatives, and φn, the n-th power of φ. Moreover, we obtain some similar estimates for the essential norms of the operators uCφ, from which sufficient and necessary conditions of compactness of uCφ follows immediately., Xin-Cui Guo, Ze-Hua Zhou., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
6. Spectra of weighted composition operators on algebras of analytic functions on Banach spaces
- Creator:
- Yuan, Cheng and Zhou, Ze-Hua
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- bounded analytic, function spaces, weighted composition operators, essential norm, and spectra
- Language:
- English
- Description:
- Let $E$ be a complex Banach space, with the unit ball $B_E$. We study the spectrum of a bounded weighted composition operator $uC_{\varphi }$ on $H^\infty (B_E)$ determined by an analytic symbol $\varphi $ with a fixed point in $B_E$ such that $\varphi (B_E)$ is a relatively compact subset of $E$, where $u$ is an analytic function on $B_E$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public