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Semi-embeddings of Banach spaces which are hereditarily c0

Published online by Cambridge University Press:  20 January 2009

L. Drewnowski
L. Drewnowski
Affiliation:
Institute of Mathematics, A. Mickiewicz University, Poznaṅ, Poland
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Following Lotz, Peck and Porta [9], a continuous linear operator from one Banach space into another is called a semi-embedding if it is one-to-one and maps the closed unit ball of the domain onto a closed (hence complete) set. (Below we shall allow the codomain to be an F-space, i.e., a complete metrisable topological vector space.) One of the main results established in [9] is that if X is a compact scattered space, then every semi-embedding of C(X) into another Banach space is an isomorphism ([9], Main Theorem, (a)⇒(b)).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 2 , June 1983 , pp. 163 - 167
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

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