Spectra of weighted algebras of holomorphic functions

Details Spectra of weighted algebras of holomorphic functions Spectra of weighted algebras of holomorphic functions

2008-02-08

arxiv.org/abs/0802.1135v2

Math. Z. 263 (2009), no. 4, 887--902

Mathematics

Functional Analysis

25 pages Corrected typos

Scientific paper

10.1007/s00209-008-0444-0

We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the spectra of weighted algebras and endow them with an analytic structure. We also deal with composition operators and algebra homomorphisms, in particular to investigate how their induced mappings act on the analytic structure of the spectrum. Moreover, a Banach-Stone type question is addressed.

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