Pointwise multiplication operators on weighted Banach spaces of analytic functions

J. Bonet; P. Domański; M. Lindström

doi:10.4064/sm-137-2-177-194

Pointwise multiplication operators on weighted Banach spaces of analytic functions

J. Bonet, P. Domański, M. Lindström

Mathematics

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

33 Citations (Scopus)

Abstract

For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator Mφ, Mφ(f) = φf, on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when Mφ is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map M'φ.

Original language	Swedish
Pages (from-to)	177-194
Number of pages	18
Journal	Studia Mathematica
Volume	137
Issue number	2
DOIs	https://doi.org/10.4064/sm-137-2-177-194
Publication status	Published - 1999
MoE publication type	A1 Journal article-refereed

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10.4064/sm-137-2-177-194

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keywords = "Approximative point spectrum, Chaotic operator, Closed range, Essential norm, Gleason part, Hypercyclic operator, Maximal ideal space of H∞, Pointwise multiplication operator, Shilov boundary, Weighted Banach spaces of analytic functions",

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AU - Domański, P.

AU - Lindström, M.

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AB - For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator Mφ, Mφ(f) = φf, on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when Mφ is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map M'φ.

KW - Approximative point spectrum

KW - Chaotic operator

KW - Closed range

KW - Essential norm

KW - Gleason part

KW - Hypercyclic operator

KW - Maximal ideal space of H∞

KW - Pointwise multiplication operator

KW - Shilov boundary

KW - Weighted Banach spaces of analytic functions

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JO - Studia Mathematica

JF - Studia Mathematica

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Pointwise multiplication operators on weighted Banach spaces of analytic functions

Abstract

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