Resumen de Holomorphic functions and polynomial ideals on Banach spaces

Daniel Carando , Verónica Dimant, Santiago Muro

• 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.