On extension of isometries between unit spheres of 𝐴𝐿_{𝑝}-spaces (0<𝑝<∞)-Reference-Cited by-同舟云学术

On extension of isometries between unit spheres of 𝐴𝐿_{𝑝}-spaces (0<𝑝<∞)

Published:2004-05-20 Issue:10 Volume:132 Page:2899-2909
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Jian Wang

Abstract

In this paper, we study the extension of isometries between unit spheres of atomic A L p AL_p -spaces ( 0 > p > ∞ , p ≠ 2 ) (0>p>\infty ,\ p\neq 2) . We find a condition under which an isometry T T between unit spheres can be linearly isometrically extended. Moreover, we prove that every onto isometry between unit spheres of atomic A L p AL_p -spaces ( 0 > p > ∞ , p ≠ 2 ) (0>p>\infty ,\ p\neq 2) can be linearly isometrically extended to the whole space.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2004-132-10/S0002-9939-04-07482-9/S0002-9939-04-07482-9.pdf

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