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Isomorphisms in Subspaces of c0

Published online by Cambridge University Press:  20 November 2018

Robert H. Lohman
Robert H. Lohman*
Affiliation:
Kent State University, Kent, Ohio
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A Banach space X is said to be subspace homogeneous if for every two isomorphic closed subspaces Y and Z of X, both of infinite codimension, there is an automorphism of X (i.e. a bounded linear bijection of X) which carries Y onto Z. In [1] Lindenstrauss and Rosenthal showed that c0 is subspace homogeneous, a property also shared by l2, and conjectured that c0 and l2 are the only subspace homogeneous Banach spaces. In that paper no mention was made of subspaces of c0.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 4 , December 1971 , pp. 571 - 572
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Lindenstrauss, J. and Rosenthal, H. P., Automorphisms in c0, l1 and m, Israel J. Math. 7 (1969), 227-239.Google Scholar
2. Pełczynski, A., Projections in certain Banach spaces, Studia Math. 19 (1960), 209-228.Google Scholar