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2. Essential norm and a new characterization of weighted composition operators from weighted Bergman spaces and Hardy spaces into the Bloch space
- Creator:
- Li, Songxiao, Qian, Ruishen, and Zhou, Jizhen
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, Bloch space, weighted Bergman space, essential norm, weighted composition operator, 13, and 51
- Language:
- English
- Description:
- In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space., Songxiao Li, Ruishen Qian, Jizhen 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. Essential norms of the Neumann operator of the arithmetical mean
- Creator:
- Král, Josef and Medková, Dagmar
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- double layer potential, Neumann’s operator of the arithmetical mean, and essential norm
- Language:
- English
- Description:
- Let K ⊂ ℝm (m ≥ 2) be a compact set; assume that each ball centered on the boundary B of K meets K in a set of positive Lebesgue measure. Let C(1) 0 be the class of all continuously differentiable real-valued functions with compact support in m and denote by σm the area of the unit sphere in m. With each ϕ ∈ C(1) 0 we associate the function WKϕ(z) = 1⁄ σm ∫ Rm\K grad ϕ(x) · z − x |z − x| m dx of the variable z ∈ K (which is continuous in K and harmonic in K \ B). WKϕ depends only on the restriction ϕ|B of ϕ to the boundary B of K. This gives rise to a linear operator WK acting from the space C(1)(B) = {ϕ|B; ϕ ∈ C(1) 0 } to the space C(B) of all continuous functions on B. The operator TK sending each f ∈ C(1)(B) to TKf = 2WKf − f ∈ C(B) is called the Neumann operator of the arithmetical mean; it plays a significant role in connection with boundary value problems for harmonic functions. If p is a norm on C(B) ⊃ C(1)(B) inducing the topology of uniform convergence and G is the space of all compact linear operators acting on C(B), then the associated p-essential norm of TK is given by ωpTK = inf Q∈G sup {p[(TK − Q)f]; f ∈ C(1)(B), p(f) ≤ 1} . In the present paper estimates (from above and from below) of ωpTK are obtained resulting in precise evaluation of ωpTK in geometric terms connected only wit K.
- 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. On Volterra composition operators from Bergman-type space to Bloch-type space
- Creator:
- Jiang, Zhi Jie
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Bergman-type space, Volterra composition operator, Bloch-type space, little Bloch-type space, and essential norm
- Language:
- English
- Description:
- Let $\varphi $ be an analytic self-mapping of $\mathbb {D}$ and $g$ an analytic function on $\mathbb {D}$. In this paper we characterize the bounded and compact Volterra composition operators from the Bergman-type space to the Bloch-type space. We also obtain an asymptotical expression of the essential norm of these operators in terms of the symbols $g$ and $\varphi $.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
7. 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