Linearization of isometric embedding on Banach spaces

Yu Zhou; Zihou Zhang; Chunyan Liu

Yu Zhou ; Zihou Zhang ; Chunyan Liu

Studia Mathematica, Tome 231 (2015), p. 31-39 / Harvested from The Polish Digital Mathematics Library

Résumé

Let X,Y be Banach spaces, f: X → Y be an isometry with f(0) = 0, and $T : \bar{s p a n} (f (X)) \to X$ be the Figiel operator with $T \circ f = I d_{X}$ 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 $\bar{s p a n} (f (X))$ is weakly nearly strictly convex.

Publié le : 2015-01-01

Zbl 06545398

EUDML-ID : urn:eudml:doc:285772

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     author = {Yu Zhou and Zihou Zhang and Chunyan Liu},
     title = {Linearization of isometric embedding on Banach spaces},
     journal = {Studia Mathematica},
     volume = {231},
     year = {2015},
     pages = {31-39},
     zbl = {06545398},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8036-12-2015}
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Yu Zhou; Zihou Zhang; Chunyan Liu. Linearization of isometric embedding on Banach spaces. Studia Mathematica, Tome 231 (2015) pp. 31-39. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8036-12-2015/