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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Analytic functions into Banach spaces and a new characterization for isomorphic embeddings


Author: V. Wrobel
Journal: Proc. Amer. Math. Soc. 85 (1982), 539-543
MSC: Primary 46G20; Secondary 30G30
MathSciNet review: 660600
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Abstract: Let $ T:E \to F$ be a continuous linear injection between complex Banach spaces. It is shown that $ T$ is a topological monomorphism if and only if every function $ f:D \to E$ on the open unit disc of the complex plane, for which $ T \circ f$ is analytic, is itself analytic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660600-X
PII: S 0002-9939(1982)0660600-X
Keywords: Banach spaces, analytic functions, isomorphic embeddings
Article copyright: © Copyright 1982 American Mathematical Society