Weighted composition operators and dynamical systems on weighted spaces of holomorphic functions on banach spaces

J. S. Manhas

doi:10.15352/afa/1399899525

Weighted composition operators and dynamical systems on weighted spaces of holomorphic functions on banach spaces

J. S. Manhas^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Let B_X and B_Y be the open unit balls of the Banach Spaces X and Y, respectively. Let V and W be two countable families of weights on B_X and B_Y, respectively. Let HV(B_X) (or HV₀ (B_X)) and HW (B_Y) (or HW₀ (B_Y)) be the weighted Fréchet spaces of holomorphic functions. In this paper, we investigate the holomorphic mappings φ: B_X → B_Y and ψ: B_X → C which characterize continuous weighted composition operators between the spaces HV (B_X) (or HV₀ (B_X)) and HW (B_Y) (or HW₀ (B_Y)). Also, we obtained a (linear) dynamical system induced by multiplication operators on these weighted spaces.

Original language	English
Pages (from-to)	58-71
Number of pages	14
Journal	Annals of Functional Analysis
Volume	4
Issue number	2
DOIs	https://doi.org/10.15352/afa/1399899525
Publication status	Published - 2013

Keywords

Dynamical system
Multiplication operator
Weight
Weighted composition operator
Weighted frechet space

ASJC Scopus subject areas

Analysis
Anatomy
Algebra and Number Theory

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abstract = "Let BX and BY be the open unit balls of the Banach Spaces X and Y, respectively. Let V and W be two countable families of weights on BX and BY, respectively. Let HV(BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)) be the weighted Fr{\'e}chet spaces of holomorphic functions. In this paper, we investigate the holomorphic mappings φ: BX → BY and ψ: BX → C which characterize continuous weighted composition operators between the spaces HV (BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)). Also, we obtained a (linear) dynamical system induced by multiplication operators on these weighted spaces.",

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T1 - Weighted composition operators and dynamical systems on weighted spaces of holomorphic functions on banach spaces

AU - Manhas, J. S.

PY - 2013

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N2 - Let BX and BY be the open unit balls of the Banach Spaces X and Y, respectively. Let V and W be two countable families of weights on BX and BY, respectively. Let HV(BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)) be the weighted Fréchet spaces of holomorphic functions. In this paper, we investigate the holomorphic mappings φ: BX → BY and ψ: BX → C which characterize continuous weighted composition operators between the spaces HV (BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)). Also, we obtained a (linear) dynamical system induced by multiplication operators on these weighted spaces.

AB - Let BX and BY be the open unit balls of the Banach Spaces X and Y, respectively. Let V and W be two countable families of weights on BX and BY, respectively. Let HV(BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)) be the weighted Fréchet spaces of holomorphic functions. In this paper, we investigate the holomorphic mappings φ: BX → BY and ψ: BX → C which characterize continuous weighted composition operators between the spaces HV (BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)). Also, we obtained a (linear) dynamical system induced by multiplication operators on these weighted spaces.

KW - Dynamical system

KW - Multiplication operator

KW - Weight

KW - Weighted composition operator

KW - Weighted frechet space

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JO - Annals of Functional Analysis

JF - Annals of Functional Analysis

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Weighted composition operators and dynamical systems on weighted spaces of holomorphic functions on banach spaces

Abstract

Keywords

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