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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A Banach subspace of $L_{1/2}$ which does not embed
in $L_1$ (isometric version)


Author: Alexander Koldobsky
Journal: Proc. Amer. Math. Soc. 124 (1996), 155-160
MSC (1991): Primary 46B04; Secondary 46E30, 60E10
MathSciNet review: 1285999
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Abstract: For every $n\geq 3,$ we construct an $n$-dimensional Banach space which is isometric to a subspace of $L_{1/2}$ but is not isometric to a subspace of $L_1.$ The isomorphic version of this problem (posed by S. Kwapien in 1969) is still open. Another example gives a Banach subspace of $L_{1/4}$ which does not embed isometrically in $L_{1/2}.$ Note that, from the isomorphic point of view, all the spaces $L_q$ with $q<1$ have the same Banach subspaces.


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Additional Information

Alexander Koldobsky
Affiliation: address Division of Mathematics and Statistics, University of Texas at San Antonio, San Antonio, Texas 78249
Email: koldobsk@ringer.cs.utsa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03010-9
PII: S 0002-9939(96)03010-9
Received by editor(s): April 28, 1994
Received by editor(s) in revised form: July 13, 1994
Communicated by: \commby Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society