Linearization of isometric embedding on Banach spaces
Volume 230 / 2015
Studia Mathematica 230 (2015), 31-39
MSC: Primary 46B04; Secondary 46B20.
DOI: 10.4064/sm8036-12-2015
Published online: 25 January 2016
Abstract
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.
