THE ALGEBRA OF BOUNDED-TYPE HOLOMORPHIC FUNCTIONS ON THE BALL

Autor(es)

Carando, Daniel ^{[1, 2]} ; Muro, Santiago ^{[1, 3]} ; Vieira, Daniela M. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Buenos Aires, Fac Cs Exactas & Nat, Dept Matemat, Buenos Aires, DF - Argentina

^[2] IMAS UBA CONICET, Buenos Aires, DF - Argentina

^[3] CIFASIS CONICET, Rosario, Santa Fe - Argentina

^[4] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 148, n. 6, p. 2447-2457, JUN 2020.
• Citações Web of Science: 0

Resumo

We study the spectrum Mb(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 l(p), 1 < p < 8, we prove that each connected component of M-b(B-lp) 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. (AU)

• Processo FAPESP: 14/07373-0 - Extensões de funções holomorfas de tipo limitado em Espaços de Banach
• Beneficiário: Daniela Mariz Silva Vieira
• Modalidade de apoio: Bolsas no Exterior - Pesquisa