Holomorphic functions and polynomial ideals on Banach spaces

Autores: Daniel Carando , Verónica Dimant, Santiago Muro
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 63, Fasc. 1, 2012, págs. 71-91
Idioma: inglés
DOI: 10.1007/s13348-010-0025-5
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Resumen
- Given {{\mathfrak{A}}} a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, {H_{b{\mathfrak{A}}}(E)} . We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum {M_{b{\mathfrak{A}}}(E)} of this algebra “behaves” like the classical case of {M_{b}(E)} (the spectrum of {H_{b}(E)}, the algebra of bounded type holomorphic functions). More precisely, we prove that {M_{b{\mathfrak{A}}}(E)} can be endowed with a structure of Riemann domain over E′′ and that the extension of each {f\in H_{b{\mathfrak{A}}}(E)} to the spectrum is an {{\mathfrak{A}}}-holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras.