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On Nonreflexive Banach Spaces Which Contain No c0 or lp

Published online by Cambridge University Press:  20 November 2018

P. G. Casazza ,
Bor-Luh Lin  and
R. H. Lohman
P. G. Casazza
Affiliation:
University of Alabama, Huntsville, Alabama
Bor-Luh Lin
Affiliation:
University of Iowa, Iowa City, Iowa
R. H. Lohman
Affiliation:
Kent State University, Kent, Ohio
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The first infinite-dimensional reflexive Banach space X such that no subspace of X is isomorphic to c0 or lp, 1 ≦ p < ∞, was constructed by Tsirelson [8]. In fact, he showed that there exists a Banach space with an unconditional basis which contains no subsymmetric basic sequence and which contains no superreflexive subspace. Subsequently, Figiel and Johnson [4] gave an analytical description of the conjugate space T of Tsirelson's example and showed that there exists a reflexive Banach space with a symmetric basis which contains no superreflexive subspace; a uniformly convex space with a symmetric basis which contains no isomorphic copy of lp, 1 < p < ∞; and a uniformly convex space which contains no subsymmetric basic sequence and hence contains no isomorphic copy of lp, 1 < p < ∞. Recently, Altshuler [2] showed that there is a reflexive Banach space with a symmetric basis which has a unique symmetric basic sequence up to equivalence and which contains no isomorphic copy of lp, 1 < p < ∞.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 6 , 01 December 1980 , pp. 1382 - 1389
Copyright
Copyright © Canadian Mathematical Society 1980

References

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