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Proceedings of the American Mathematical Society

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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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  • [1] R. Aron and J. A. Cima, A theorem on holomorphic mappings into Banach spaces with basis, Proc. Amer. Math. Soc. 36 (1972), 289-292. MR 0317046 (47:5594)
  • [2] J. Globevnik, On analytic functions into $ {l^p}$-spaces, Proc. Amer. Math. Soc. 61 (1976), 73-76. MR 0425138 (54:13095)
  • [3] V. Wrobel, Streng singuläre Operatoren in lokalkonvexen Räumen, Math. Nachr. 83 (1978), 127-142. MR 506851 (80i:47031)

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Keywords: Banach spaces, analytic functions, isomorphic embeddings
Article copyright: © Copyright 1982 American Mathematical Society

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