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 ? a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, ???(?) . We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum ???(?) 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 ???(?) can be endowed with a structure of Riemann domain over E′′ and that the extension of each ?∈???(?) to the spectrum is an ? -holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras.