6533b82bfe1ef96bd128cedd

RESEARCH PRODUCT

A Riemann manifold structure of the spectra of weighted algebras of holomorphic functions

Domingo GarcíaDaniel CarandoManuel MaestrePablo Sevilla-peris

subject

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsFréchet algebraWeighted space of holomorphic functionsHolomorphic functional calculusInfinite-dimensional vector functionSpectrum (functional analysis)Holomorphic functionFrechet algebraBanach manifoldAnalytic manifold structureAnalytic manifoldBergman spaceSymmetrically regular Banach spaceGeometry and TopologyMATEMATICA APLICADAWeighted spaceMathematics

description

[EN] In this paper we give general conditions on a countable family V of weights on an unbounded open set U in a complex Banach space X such that the weighted space HV (U) of holomorphic functions on U has a Frechet algebra structure. For such weights it is shown that the spectrum of HV(U) has a natural analytic manifold structure when X is a symmetrically regular Banach space, and in particular when X = C-n. (C) 2009 Elsevier Ltd. All rights reserved.

yearjournalcountryeditionlanguage
2009-06-01Topology
10.1016/j.top.2009.11.003http://dx.doi.org/10.1016/j.top.2009.11.003