Linearization of isometric embedding on Banach spaces

Yu Zhou, Zihou Zhang, and Chunyan Liu. "Linearization of isometric embedding on Banach spaces." Studia Mathematica 230.1 (2015): 31-39. <http://eudml.org/doc/285772>.

@article{YuZhou2015,
abstract = {Let X,Y be Banach spaces, f: X → Y be an isometry with f(0) = 0, and $T: \overline\{span\}(f(X)) → X$ be the Figiel operator with $T ∘ f = Id_\{X\}$ 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 $\overline\{span\}(f(X))$ is weakly nearly strictly convex.},
author = {Yu Zhou, Zihou Zhang, Chunyan Liu},
journal = {Studia Mathematica},
keywords = {isometry; linearly isometric right inverse; Figiel operator; Banach space},
language = {eng},
number = {1},
pages = {31-39},
title = {Linearization of isometric embedding on Banach spaces},
url = {http://eudml.org/doc/285772},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Yu Zhou
AU - Zihou Zhang
AU - Chunyan Liu
TI - Linearization of isometric embedding on Banach spaces
JO - Studia Mathematica
PY - 2015
VL - 230
IS - 1
SP - 31
EP - 39
AB - Let X,Y be Banach spaces, f: X → Y be an isometry with f(0) = 0, and $T: \overline{span}(f(X)) → X$ be the Figiel operator with $T ∘ f = Id_{X}$ 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 $\overline{span}(f(X))$ is weakly nearly strictly convex.
LA - eng
KW - isometry; linearly isometric right inverse; Figiel operator; Banach space
UR - http://eudml.org/doc/285772
ER -