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Spectra of weighted algebras of holomorphic functions

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Abstract

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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Authors and Affiliations

  1. Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, 1428, Buenos Aires, Argentina

    Daniel Carando

  2. Departamento de Matemática Aplicada and IUMPA, ETSMRE, Universidad Politécnica de Valencia, Av. Blasco Ibáñez, 21, 46010, Valencia, Spain

    Pablo Sevilla-Peris

Authors
  1. Daniel Carando
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  2. Pablo Sevilla-Peris
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Correspondence to Daniel Carando.

Additional information

D. Carando was supported by UBACyT X038, PICT 05-33042 and PICT 06-00587 and CONICET.

P. Sevilla-Peris was supported by the MECD Project MTM2005-08210.

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Carando, D., Sevilla-Peris, P. Spectra of weighted algebras of holomorphic functions. Math. Z. 263, 887–902 (2009). https://doi.org/10.1007/s00209-008-0444-0

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  • DOI: https://doi.org/10.1007/s00209-008-0444-0

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