Algebras of entire functions containing functions of unbounded type on a Banach space

Keywords: analytic function on a Banach space, function of unbounded type, spectra of an algebra of analytic functions
Published online: 2021-09-26


In this paper, we consider algebras of entire analytic functions which are bounded on a prescribed family of balls in a Banach space. We investigate the structures of such algebras and describe their spectra in terms of spectra of algebras of uniformly continuous analytic functions. Some partial examples are considered. In particular, we have complete descriptions of the spectra for the case of Tsirelson space and for $c_0$.

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How to Cite
ZagorodnyukA.; HihliukA. Algebras of Entire Functions Containing Functions of Unbounded Type on a Banach Space. Carpathian Math. Publ. 2021, 13, 426-432.