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January 2019 On the unit sphere of positive operators
Antonio M. Peralta
Banach J. Math. Anal. 13(1): 91-112 (January 2019). DOI: 10.1215/17358787-2018-0017

Abstract

Given a C -algebra A , let S ( A + ) denote the set of positive elements in the unit sphere of A . Let H 1 , H 2 , H 3 , and H 4 be complex Hilbert spaces, where H 3 and H 4 are infinite-dimensional and separable. In this article, we prove a variant of Tingley’s problem by showing that every surjective isometry Δ : S ( B ( H 1 ) + ) S ( B ( H 2 ) + ) (resp., Δ : S ( K ( H 3 ) + ) S ( K ( H 4 ) + ) ) admits a unique extension to a surjective complex linear isometry from B ( H 1 ) onto B ( H 2 ) (resp., from K ( H 3 ) onto K ( H 4 ) ). This provides a positive answer to a conjecture recently posed by Nagy.

Citation

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Antonio M. Peralta. "On the unit sphere of positive operators." Banach J. Math. Anal. 13 (1) 91 - 112, January 2019. https://doi.org/10.1215/17358787-2018-0017

Information

Received: 13 April 2018; Accepted: 21 May 2018; Published: January 2019
First available in Project Euclid: 30 October 2018

zbMATH: 07002033
MathSciNet: MR3892338
Digital Object Identifier: 10.1215/17358787-2018-0017

Subjects:
Primary: 47B49
Secondary: 46A16, 46A22‎, 46B04, 46B20, 46E40

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 1 • January 2019
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