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

DANIEL CARANDO; DOMINGO GARCÍA; MANUEL MAESTRE; PABLO SEVILLA PERIS

TOPOLOGY

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2009 vol. 48 p. 54 - 65

0040-9383

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 Fr´{e}chet  algebra structure. For that kind of weights it is shown that the spectrum of $HV(U)$ has a natural analytic manifold structure  when $X$ is a symmetrically regular Banach space, in particular when $X=C^n$.