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Reinhardt domains of holomorphy in Banach spaces

✍ Scribed by Mário C Matos; Leopoldo Nachbin

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
643 KB
Volume
92
Category
Article
ISSN
0001-8708

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✦ Synopsis

It is known that in c0 the holomorphic functions representable by multiple power series (the series of monomials) are those of nuclear type. In this article we show that in a Banach space with unconditional Schauder basis every domain of existence is the domain of existence of a holomorphic function representable by a multiple power series and, in fact, the domain of convergence of such a series.

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✍ Luis Bernal-González 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 133 KB

In this note the following new version of the Schwarz lemma is proved: If f is a holomorphic function mapping a bounded convex domain D D of a complex Banach 1 Ž . space into a convex domain D D of another complex Banach space and f a s b, 2 then the image by f of the set of points in D D lying at a