A solution to Tingley's problem for isometries between the unit spheres of compact C*-algebras and JB*-triples

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（3）
• 页码范围: 553-568
• 页数: 16页
• 语种: 英文

摘要

Let f:S(E) → S(B) be a surjective isometry between the unit spheres of two weakly compact JB*-triples not containing direct summands of rank less than or equal to 3.Suppose E has rank greater than or equal to 5.Applying techniques developed in JB*-triple theory,we prove that f admits an extension to a surjective real linear isometry T:E → B.Among the consequences,we show that every surjective isometry between the unit spheres of two compact C*-algebras A and B,without assuming any restriction on the rank of their direct summands (and in particular when A =K(H) and B =K(H')),extends to a surjective real linear isometry from A into B.These results provide new examples of infinite-dimensional Banach spaces where Tingley's problem admits a positive answer.