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2. 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
3. Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space $H^{2}$
- Creator:
- Fatehi, Mahsa and Robati, Bahram Khani
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Hardy spaces, essentially normal, composition operator, and linear-fractional transformation
- Language:
- English
- Description:
- In 1999 Nina Zorboska and in 2003 P. S. Bourdon, D. Levi, S. K. Narayan and J. H. Shapiro investigated the essentially normal composition operator $C_{\varphi }$, when $\varphi $ is a linear-fractional self-map of $\mathbb {D}$. In this paper first, we investigate the essential normality problem for the operator $T_{w}C_{\varphi }$ on the Hardy space $H^{2}$, where $w$ is a bounded measurable function on $\partial \mathbb {D}$ which is continuous at each point of $F(\varphi )$, $\varphi \in {\cal S}(2)$, and $T_{w}$ is the Toeplitz operator with symbol $w$. Then we use these results and characterize the essentially normal finite linear combinations of certain linear-fractional composition operators on $H^{2}$.
- 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. Numerical range of operators acting on Banach spaces
- Creator:
- Jahedi, Khadijeh and Yousefi, Bahmann
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- numerical range, weighted Hardy space, compact operator, and composition operator
- Language:
- English
- Description:
- The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small weighted Hardy space has zero.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
6. Operators on Lorentz sequence spaces
- Creator:
- Arora, S. C, Datt, Gopal, and Verma, Satish
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- composition operator, distribution function, Fredholm operator, Lorentz space, Lorentz sequence space, multiplication operator, and non-increasing rearrangement
- Language:
- English
- Description:
- Description of multiplication operators generated by a sequence and composition operators induced by a partition on Lorentz sequence spaces l(p, q), 1 < p ≤ ∞, 1 ≤ q ≤ ∞ is presented.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
7. Some equivalent metrics for bounded normal operators
- Creator:
- Jabbarzadeh, Mohammad Reza and Hajipouri, Rana
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Hilbert space, normal operator, equivalent metrics, and composition operator
- Language:
- English
- Description:
- Some stronger and equivalent metrics are defined on M, the set of all bounded normal operators on a Hilbert space H and then some topological properties of M are investigated.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8. Strictly cyclic algebra of operators acting on Banach spaces $H^p(\beta)$
- Creator:
- Yousefi, Bahmann
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- the Banach space of formal power series associated with a sequence $\beta $, bounded point evaluation, strictly cyclic maximal ideal space, Schatten $p$-class, reflexive algebra, semisimple algebra, and composition operator
- Language:
- English
- Description:
- Let $\lbrace \beta (n)\rbrace ^{\infty }_{n=0}$ be a sequence of positive numbers and $1 \le p < \infty $. We consider the space $H^{p}(\beta )$ of all power series $f(z)=\sum ^{\infty }_{n=0}\hat{f}(n)z^{n}$ such that $\sum ^{\infty }_{n=0}|\hat{f}(n)|^{p}\beta (n)^{p} < \infty $. We investigate strict cyclicity of $H^{\infty }_{p}(\beta )$, the weakly closed algebra generated by the operator of multiplication by $z$ acting on $H^{p}(\beta )$, and determine the maximal ideal space, the dual space and the reflexivity of the algebra $H^{\infty }_{p}(\beta )$. We also give a necessary condition for a composition operator to be bounded on $H^{p}(\beta )$ when $H^{\infty }_{p}(\beta )$ is strictly cyclic.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public