The Mazur-Ulam property in l(infinity)-sum and c(0)-sum of strictly convex Banach spaces

摘要

In this paper we deal with those Banach spaces Zwhich satisfy the Mazur-Ulam property, namely that every surjective isometry Delta from the unit sphere of Z to the unit sphere of any Banach space Yadmits a unique extension to a surjective real-linear isometry from Zto Y. We prove that for every countable set Gwith vertical bar Gamma vertical bar >= 2, the Banach space circle plus(c0)(gamma epsilon Gamma) X-gamma satisfies the Mazur-Ulam property, whenever the Banach space X-gamma is strictly convex with dim((X-gamma)(R)) >= 2 for every gamma. As a consequence, every weakly countably determined Banach space can be equivalently renormed so that it satisfies the Mazur-Ulam property. (C) 2020 Published by Elsevier Inc.