Weighted composition operators between weighted spaces of vector-valued holomorphic functions on Banach spaces

J. S. Manhas

doi:10.1016/j.amc.2011.03.131

Weighted composition operators between weighted spaces of vector-valued holomorphic functions on Banach spaces

J. S. Manhas^*

^*Corresponding author for this work

Mathematics & Statistics

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

1 Citation (Scopus)

Abstract

Let B(E, F) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let U_X and U_Y be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on U_X and U_Y, respectively. Let HV(U_X, E) (or HV₀(U_X, E)) and HW(U_Y, F) (or HW₀(U_Y, F)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings φ: U_Y → U_X and ψ: U_Y → B(E, F) which generate weighted composition operators between these weighted spaces.

Original language	English
Pages (from-to)	929-934
Number of pages	6
Journal	Applied Mathematics and Computation
Volume	218
Issue number	3
DOIs	https://doi.org/10.1016/j.amc.2011.03.131
Publication status	Published - Oct 1 2011

Keywords

Nachbin families
Vector-valued holomorphic functions
Weighted composition operators
Weighted spaces
Weights

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics

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10.1016/j.amc.2011.03.131

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abstract = "Let B(E, F) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let UX and UY be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on UX and UY, respectively. Let HV(UX, E) (or HV0(UX, E)) and HW(UY, F) (or HW0(UY, F)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings φ: UY → UX and ψ: UY → B(E, F) which generate weighted composition operators between these weighted spaces.",

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AB - Let B(E, F) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let UX and UY be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on UX and UY, respectively. Let HV(UX, E) (or HV0(UX, E)) and HW(UY, F) (or HW0(UY, F)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings φ: UY → UX and ψ: UY → B(E, F) which generate weighted composition operators between these weighted spaces.

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KW - Weighted spaces

KW - Weights

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Weighted composition operators between weighted spaces of vector-valued holomorphic functions on Banach spaces

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