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Proceedings of the American Mathematical Society

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Banach spaces failing the almost isometric universal extension property

Author: D. M. Speegle
Journal: Proc. Amer. Math. Soc. 126 (1998), 3633-3637
MSC (1991): Primary 46B20
MathSciNet review: 1458266
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Abstract: If $X$ is an infinite dimensional, separable, uniformly smooth Banach space, then there is an $\epsilon > 0$, a Banach space $Y$ containing $X$ as a closed subspace and a norm one map $T$ from $X$ to a $C(K)$ space which does not extend to an operator $\tilde T$ from $Y$ to $C(K)$ with $\|\tilde T\| \le 1+\epsilon $.

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Additional Information

D. M. Speegle
Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843
Address at time of publication: Department of Mathematics, Saint Louis University, Saint Louis, Missouri 63103

Received by editor(s): December 23, 1996
Received by editor(s) in revised form: April 25, 1997
Additional Notes: The author was supported in part by the NSF through the Workshop in Linear Analysis and Probability at Texas A&M
Communicated by: Dale Alspach
Article copyright: © Copyright 1998 American Mathematical Society