Let $X,Y$ be Banach spaces, $f:X\rightarrow Y$ be an isometry with $f(0)=0$, and $T:\overline {\rm span}(f(X))\rightarrow X$ be the Figiel operator with $T\circ f={\rm Id}_X$ and $\|T\| =1$. We present a sufficient and necessary condition for the Figiel operator $T$ to admit a linear isometric right inverse. We also prove that such a right inverse exists when $\overline {\rm span}(f(X))$ is weakly nearly strictly convex.
1
College of Fundamental Studies Shanghai University of Engineering Science Shanghai, 201620, China
Yu Zhou; Zihou Zhang; Chunyan Liu. Linearization of isometric embedding on Banach spaces. Studia Mathematica, Tome 230 (2015) no. 1, pp. 31-39. doi: 10.4064/sm8036-12-2015
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author = {Yu Zhou and Zihou Zhang and Chunyan Liu},
title = {Linearization of isometric embedding on {Banach} spaces},
journal = {Studia Mathematica},
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year = {2015},
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doi = {10.4064/sm8036-12-2015},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm8036-12-2015/}
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