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Weighted composition operators on weighted spaces of vector-valued analytic functions

Jasbir Singh Manhas
대한수학회 (The Korean Mathematical Society)|2008.09|대한수학회지 (Journal of the KMS)|제45권 제5호|pp. 1203-1220

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참고문헌

키워드

Banach algebraweighted composition operatorssystem of weightsinvertible and compact operators
주제분류수학

초록

Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb (G,E) and HV0 (G,E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings φ : G → G and operator-valued analytic mappings Ψ : G → B (E) which generate weighted composition operators and invertible weighted composition operators on the spaces HVb (G,E) and HV0 (G,E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.

Abstract

Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb (G,E) and HV0 (G,E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings φ : G → G and operator-valued analytic mappings Ψ : G → B (E) which generate weighted composition operators and invertible weighted composition operators on the spaces HVb (G,E) and HV0 (G,E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.

참고문헌 (36)

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