scholarly journals Essential Norm of Operators into Weighted-Type Spaces on the Unit Ball

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Pablo Galindo ◽  
Mikael Lindström ◽  
Stevo Stević
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Type Space ◽  
Type Spaces ◽  
Weighted Type ◽  
General Banach Space

The essential norm of any operator from a general Banach space of holomorphic functions on the unit ball inℂninto the little weighted-type space is calculated. Some applications of the formula are given.

scholarly journals New characterizations for differences of composition operators between weighted-type spaces in the unit ball

2021 ◽  
Vol 73 (8) ◽  
pp. 1129-1139
Author(s):  
C. Chen
Keyword(s):  
Unit Ball ◽  
Necessary Conditions ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Spaces Of Holomorphic Functions ◽  
Type Spaces ◽  
Sufficient And Necessary Conditions ◽  
Weighted Type ◽  
Equivalent Expressions

In this paper, we present some asymptotically equivalent expressions to the essential norm of differences of composition operators acting on weighted-type spaces of holomorphic functions in the unit ball of . Especially, the descriptions in terms of are described. From which the sufficient and necessary conditions of compactness follows immediately. Also, we characterize the boundedness of these operators.

scholarly journals Weighted Iterated Radial Composition Operators between Some Spaces of Holomorphic Functions on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Mixed Norm ◽  
Mixed Norm Space ◽  
Type Space ◽  
Spaces Of Holomorphic Functions ◽  
Schmidt Norm ◽  
Norm Space ◽  
Weighted Type

The boundedness and compactness of weighted iterated radial composition operators from the mixed-norm space to the weighted-type space and the little weighted-type space on the unit ball are characterized here. We also calculate the Hilbert-Schmidt norm of the operator on the weighted Bergman-Hilbert space as well as on the Hardy space.

scholarly journals Essential Norms of Weighted Composition Operators from theα-Bloch Space to a Weighted-Type Space on the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Lower And Upper Bounds ◽  
Type Space ◽  
Weighted Composition ◽  
Weighted Type

This paper finds some lower and upper bounds for the essential norm of the weighted composition operator fromα-Bloch spaces to the weighted-type spaceHμ∞on the unit ball for the caseα≥1.

scholarly journals On a New Integral-Type Operator from the Weighted Bergman Space to the Bloch-Type Space on the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Weighted Bergman Space ◽  
Type Operator ◽  
Upper And Lower Bounds ◽  
Integral Type ◽  
Type Space ◽  
Bloch Type Space

We introduce an integral-type operator, denoted byPφg, on the space of holomorphic functions on the unit ballB⊂ℂn, which is an extension of the product of composition and integral operators on the unit disk. The operator norm ofPφgfrom the weighted Bergman spaceAαp(B)to the Bloch-type spaceℬμ(B)or the little Bloch-type spaceℬμ,0(B)is calculated. The compactness of the operator is characterized in terms of inducing functionsgandφ. Upper and lower bounds for the essential norm of the operatorPφg:Aαp(B)→ℬμ(B), whenp>1, are also given.

scholarly journals Hadamard gap series in weighted-type spaces on the unit ball

2017 ◽  
Vol 8 (2) ◽  
pp. 259-269 ◽  
Author(s):  
Bingyang Hu ◽  
Songxiao Li
Keyword(s):  
Unit Ball ◽  
Gap Series ◽  
Type Spaces ◽  
Weighted Type

scholarly journals ESSENTIAL NORM OF EXTENDED CESÀRO OPERATORS FROM ONE BERGMAN SPACE TO ANOTHER

2011 ◽  
Vol 85 (2) ◽  
pp. 307-314 ◽  
Author(s):  
ZHANGJIAN HU
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Normal Weight ◽  
Cesàro Operator ◽  
Radial Derivative ◽  
Image Position ◽  
Cesaro Operator

AbstractLet Ap(φ) be the pth Bergman space consisting of all holomorphic functions f on the unit ball B of ℂn for which $\|f\|^p_{p,\varphi }= \int _B |f(z)|^p \varphi (z) \,dA(z)\lt +\infty $, where φ is a given normal weight. Let Tg be the extended Cesàro operator with holomorphic symbol g. The essential norm of Tg as an operator from Ap (φ) to Aq (φ) is denoted by $\|T_g\|_{e, A^p (\varphi )\to A^q (\varphi )} $. In this paper it is proved that, for p≤q, with 1/k=(1/p)−(1/q) , where ℜg(z) is the radial derivative of g; and for p>q, with 1/s=(1/q)−(1/p) .

scholarly journals The strict topology on spaces of bounded holomorphic functions

1994 ◽  
Vol 49 (2) ◽  
pp. 249-256 ◽  
Author(s):  
Juan Ferrera ◽  
Angeles Prieto
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Holomorphic Functions ◽  
Open Unit ◽  
Strict Topology ◽  
Open Unit Ball ◽  
Approximation By Polynomials ◽  
Bounded Holomorphic

We introduce in this paper the space of bounded holomorphic functions on the open unit ball of a Banach space endowed with the strict topology. Some good properties of this topology are obtained. As applications, we prove some results on approximation by polynomials and a description of the continuous homomorphisms.

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