Geodesic
Isometric Stability Property of Certain Banach Spaces
Canadian mathematical bulletin, Tome 38 (1995) no. 1, pp. 93-97

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DOI

Let E be one of the spaces C(K) and L 1, F be an arbitrary Banach space, p > 1, and (X, σ) be a space with a finite measure. We prove that E is isometric to a subspace of the Lebesgue-Bochner space LP(X; F) only if E is isometric to a subspace of F. Moreover, every isometry T from E into Lp(X; F) has the form Te(x) = h(x)U(x)e, e ∊ E, where h: X —> R is a measurable function and, for every x ∊ X, U(x) is an isometry from E to F
DOI : 10.4153/CMB-1995-012-9
Mots-clés : 46B04, 47B80, isometries, Lebesgue-Bochner spaces, random operators 
Koldobsky, Alexander. Isometric Stability Property of Certain Banach Spaces. Canadian mathematical bulletin, Tome 38 (1995) no. 1, pp. 93-97. doi: 10.4153/CMB-1995-012-9
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     author = {Koldobsky, Alexander},
     title = {Isometric {Stability} {Property} of {Certain} {Banach} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {93--97},
     year = {1995},
     volume = {38},
     number = {1},
     doi = {10.4153/CMB-1995-012-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-012-9/}
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