INVESTIGADORES
MURO Luis Santiago Miguel
artículos
Título:
Envelopes of holomorphy and extension of functions of bounded type
Autor/es:
CARANDO, DANIEL; MURO, SANTIAGO
Revista:
ADVANCES IN MATHEMATICS
Editorial:
ACADEMIC PRESS INC ELSEVIER SCIENCE
Referencias:
Año: 2012
ISSN:
0001-8708
Resumen:
In this article we characterize the envelope of holomorphy for the algebra of bounded type holomorphic functions on Riemann domains over a Banach space in terms of the spectrum of the algebra. We prove that evaluations at points of the envelope are always continuous but we show an example of a balanced open subset of $c_0$ where the extensions to the envelope are not necessarily of bounded type, answering a question posed by Hirschowitz in 1972. We show that for bounded balanced sets the extensions are of bounded type. We also consider extensions to the bidual, and show some properties of the spectrum in the case of the unit ball of $ell_p$.
