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Semi-embeddings of Banach space

Published online by Cambridge University Press:  20 January 2009

Heinrich P. Lotz ,
N. T. Peck  and
Horacio Porta
Heinrich P. Lotz
Affiliation:
University of Illinois, Urbana, Illinois
N. T. Peck
Affiliation:
University of Illinois, Urbana, Illinois
Horacio Porta
Affiliation:
University of Illinois, Urbana, Illinois
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It is a most implausible fact that a one-to-one operator from c0 into a Banach space which maps the unit ball of c0 onto a closed set is necessarily an isomorphism.

In this paper the term semi-embedding denotes a one-to-one operator from one Banach space into another, which maps the closed unit ball of the domain onto a closed set. In the first section we study semi-embeddings in conjunction with weak compactness; in the second section we apply our results to the case of semi-embeddings defined on C(X), X compact.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 3 , October 1979 , pp. 233 - 240
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

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