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Linearization of isometric embedding on Banach spaces

Volume 230 / 2015

Yu Zhou, Zihou Zhang, Chunyan Liu 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.

Authors

  • Yu ZhouCollege of Fundamental Studies
    Shanghai University of Engineering Science
    Shanghai, 201620, China
    e-mail
  • Zihou ZhangCollege of Fundamental Studies
    Shanghai University of Engineering Science
    Shanghai, 201620, China
    e-mail
  • Chunyan LiuCollege of Fundamental Studies
    Shanghai University of Engineering Science
    Shanghai, 201620, China
    e-mail

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