The algebra of bounded-type holomorphic functions on the ball

CARANDO, DANIEL; MURO, SANTIAGO; VIEIRA, DANIELA M.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Año: 2020 vol. 148 p. 2447 - 2457

0002-9939

We study the spectrum $ M_b(U)$ of the algebra of bounded-type holomorphic functions on a complete Reinhardt domain in a symmetrically regular Banach space $ E$ as an analytic manifold over the bidual of the space. In the case that $ U$ is the unit ball of $ \ell _p$, $ 1<p<\infty $, we prove that each connected component of $ M_b(B_{\ell _p})$ naturally identifies with a ball of a certain radius. We also provide estimates for this radius and in many natural cases we have the precise value. As a consequence, we obtain that for connected components different from that of evaluations, these radii are strictly smaller than one, and can be arbitrarily small. We also show that for other Banach sequence spaces, connected components do not necessarily identify with balls.