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

 

Complemented isometric copies of $L_{1}$ in dual Banach spaces


Author: J. Hagler
Journal: Proc. Amer. Math. Soc. 130 (2002), 3313-3324
MSC (2000): Primary 46B04, 46B10; Secondary 46B20
Published electronically: March 25, 2002
MathSciNet review: 1913011
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Abstract: Let $X$ be a real or complex Banach space and $K\geq1$. Then $X^{\ast}$contains a $K$-complemented, isometric copy of $L_{1}\left[ 0,1\right] $ if and only if $X^{\ast}$ contains a $K$-complemented, isometric copy of $C\left[0,1\right] ^{\ast}$ if and only if $X$ contains a subspace $\left( 1,K\right) $-asymptotic to $\left( \ell_{1}\oplus\sum_{n}\ell_{\infty} ^{n}\right)_{1}$.


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Additional Information

J. Hagler
Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
Email: jhagler@math.du.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06474-2
PII: S 0002-9939(02)06474-2
Keywords: Banach spaces, complemented isometric copies of $L_1$, $\left( 1,K\right) $\emph{-}asymptotic copies of\emph{ }$\left( \ell_{1}\oplus\sum_{n}\ell_{\infty}^{n}\right) _{1}$
Received by editor(s): January 30, 2001
Received by editor(s) in revised form: June 13, 2001
Published electronically: March 25, 2002
Additional Notes: The author would especially like to thank H. P. Rosenthal and C. Stegall. Thanks also go to M. Girardi, S. Dilworth, W. B.\ Johnson and the referee for helpful comments and suggestions
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2002 American Mathematical Society