Complemented isometric copies of $L_{1}$ in dual Banach spaces
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- by J. Hagler PDF
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Abstract:
Let $X$ be a real or complex Banach space and $K\geq 1$. 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 $\left ( \ell _{1}\oplus \sum _{n}\ell _{\infty } ^{n}\right )_{1}$.References
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Additional Information
- J. Hagler
- Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
- Email: jhagler@math.du.edu
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3313-3324
- MSC (2000): Primary 46B04, 46B10; Secondary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-02-06474-2
- MathSciNet review: 1913011