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- W2513298779 abstract "Let $f: S(E) to S(B)$ be a surjective isometry between the unit spheres of two weakly compact JB$^*$-triples not containing direct summands of rank smaller 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 $T: Eto B$. Among the consequences, we show that every surjective isometry between the unit spheres of two compact C$^*$-algebras $A$ and $B$ (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." @default.
- W2513298779 created "2016-09-16" @default.
- W2513298779 creator A5055101996 @default.
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- W2513298779 date "2018-09-03" @default.
- W2513298779 modified "2023-09-26" @default.
- W2513298779 title "A solution to Tingley’s problem for isometries between the unit spheres of compact C*-algebras and JB*-triples" @default.
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- W2513298779 doi "https://doi.org/10.1007/s11425-017-9188-6" @default.
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