scholarly journals Composition Operators and Multiplication Operators on Weighted Spaces of Analytic Functions

2007 ◽  
Vol 2007 ◽  
pp. 1-21 ◽  
Author(s):  
J. S. Manhas
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Linear Operators ◽  
Weighted Spaces ◽  
Multiplication Operators ◽  
Arbitrary System ◽  
Bounded Linear ◽  
Vector Valued ◽  
Locally Convex ◽  
Spaces Of Analytic Functions

LetVbe an arbitrary system of weights on an open connected subsetGofℂN(N≥1)and letB(E)be the Banach algebra of all bounded linear operators on a Banach spaceE. LetHVb(G,E)andHV0(G,E)be the weighted locally convex spaces of vector-valued analytic functions. In this survey, we present a development of the theory of multiplication operators and composition operators from classical spaces of analytic functionsH(G)to the weighted spaces of analytic functionsHVb(G,E)andHV0(G,E).

scholarly journals Multiplication operators on weighted spaces of vector-valued continuous functions

1991 ◽  
Vol 50 (1) ◽  
pp. 98-107 ◽  
Author(s):  
R. K. Singh ◽  
Jasbir Singh Manhas
Keyword(s):  
Convex Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Weighted Spaces ◽  
Multiplication Operators ◽  
Supremum Norm ◽  
Locally Convex Spaces ◽  
Completely Regular ◽  
Vector Valued ◽  
Locally Convex

AbstractIf V is a system of weights on a completely regular Hausdorff space X and E is alocally convex space, then CV0(X, E) and CVb (X, E) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.

scholarly journals On a Class of Composition Operators on Bergman Space

2007 ◽  
Vol 2007 ◽  
pp. 1-11
Author(s):  
Namita Das ◽  
R. P. Lal ◽  
C. K. Mohapatra
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Measurable Function ◽  
Analytic Functions ◽  
Composition Operators ◽  
Linear Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Bounded Linear

Let&#x1D53B;={z∈ℂ:|z|<1}be the open unit disk in the complex planeℂ. LetA2(&#x1D53B;)be the space of analytic functions on&#x1D53B;square integrable with respect to the measuredA(z)=(1/π)dx dy. Givena∈&#x1D53B;andfany measurable function on&#x1D53B;, we define the functionCafbyCaf(z)=f(ϕa(z)), whereϕa∈Aut(&#x1D53B;). The mapCais a composition operator onL2(&#x1D53B;,dA)andA2(&#x1D53B;)for alla∈&#x1D53B;. Letℒ(A2(&#x1D53B;))be the space of all bounded linear operators fromA2(&#x1D53B;)into itself. In this article, we have shown thatCaSCa=Sfor alla∈&#x1D53B;if and only if∫&#x1D53B;S˜(ϕa(z))dA(a)=S˜(z), whereS∈ℒ(A2(&#x1D53B;))andS˜is the Berezin symbol of S.

Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

1999 ◽  
Vol 42 (2) ◽  
pp. 139-148 ◽  
Author(s):  
José Bonet ◽  
Paweł Dománski ◽  
Mikael Lindström
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Point Evaluation ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractEvery weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

scholarly journals Comparison of singular numbers of composition operators on different Hilbert spaces of analytic functions

2021 ◽  
Vol 280 (3) ◽  
pp. 108834
Author(s):  
Pascal Lefèvre ◽  
Daniel Li ◽  
Hervé Queffélec ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Hilbert Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Singular Numbers ◽  
Spaces Of Analytic Functions

scholarly journals Weighted composition operators between weak spaces of vector-valued analytic functions

Analysis ◽  
2017 ◽  
Vol 37 (1) ◽  
Author(s):  
Mostafa Hassanlou ◽  
Jussi Laitila ◽  
Hamid Vaezi
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Vector Valued

AbstractWe consider weighted composition operators

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