Low rank compact operators and Tingley's problem
By Francisco J. Fern'andez-Polo, Antonio M. Peralta. Advances in Mathematics, 2016
61 citations recorded by the source corpus.
Let $E$ and $B$ be arbitrary weakly compact JB$^*$-triples whose unit spheres are denoted by $S(E)$ and $S(B)$, respectively. We prove that every surjective isometry $f: S(E) \to S(B)$ admits an extension to a surjective real linear isometry $T: E\to B$. This is a complete solution to Tingley's problem in the setting of weakly compact JB$^*$-triples. Among the consequences, we show that if $K(H,K)$ denotes the space of compact operators between arbitrary complex Hilbert spaces $H$ and $K$, then every surjective isometry $f: S(K(H,K)) \to S(K(H,K))$ admits an extension to a surjective real linear isometry $T: K(H,K)\to K(H,K)$.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/55d58fddbde403db4f6c31d452ce502365557cc1
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- A survey on Tingley’s problem for operator algebras (2018, background): “We strive for conciseness and for restrict the results to the setting of operator algebras, despite that some of the results have been already extended to the strictly wider setting of JB-triples (compare [24, 26]).”