Banach spaces failing the almost isometric universal extension property

Speegle, D.

doi:10.1090/S0002-9939-98-04517-1

Banach spaces failing the almost isometric universal extension property
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by D. M. Speegle PDF

Proc. Amer. Math. Soc. 126 (1998), 3633-3637 Request permission

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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