Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 37, 2012, 445-460

ALGEBRAS OF FUNCTIONS WITH PRESCRIBED RADII OF BOUNDEDNESS AND THE SPECTRA OF H(U)

Domingo García, Manuel Maestre and Ignacio Zalduendo

Universidad de Valencia, Departamento de Análisis Matemático
46100 Burjasot, Valencia, Spain; Domingo.Garcia 'at' uv.es

Universidad de Valencia, Departamento de Análisis Matemático
46100 Burjasot, Valencia, Spain; Manuel.Maestre 'at' uv.es

Universidad Torcuato Di Tella, Departamento de Matemática
Miñones 2177 (C1428ATG), Buenos Aires, Argentina; nacho 'at' utdt.edu

Abstract. We study the spectra of algebras of holomorphic functions with prescribed radii of boundedness, and use these results to study the tau_omega and tau_delta spectra of H(U), where U is an open subset of a non-separable Banach space. We construct tau_delta-continuous characters on H(U) which are not evaluations at points of U. We also discuss subsets of ell_\infty which are bounding for H(U), U \subset ell_\infty.

2010 Mathematics Subject Classification: Primary 46G20; Secondary 46E25.

Key words: Holomorphic function, spectrum, Banach space.

Reference to this article: D. García, M. Maestre and I. Zalduendo: Algebras of functions with prescribed radii of boundedness and the spectra of H(U). Ann. Acad. Sci. Fenn. Math. 37 (2012), 445-460.

Full document as PDF file

doi:10.5186/aasfm.2012.3727

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