Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 13, Number 1 (2019), 91-112.
On the unit sphere of positive operators
Given a -algebra , let denote the set of positive elements in the unit sphere of . Let , , , and be complex Hilbert spaces, where and are infinite-dimensional and separable. In this article, we prove a variant of Tingley’s problem by showing that every surjective isometry (resp., ) admits a unique extension to a surjective complex linear isometry from onto (resp., from onto ). This provides a positive answer to a conjecture recently posed by Nagy.
Banach J. Math. Anal., Volume 13, Number 1 (2019), 91-112.
Received: 13 April 2018
Accepted: 21 May 2018
First available in Project Euclid: 30 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47B49: Transformers, preservers (operators on spaces of operators)
Secondary: 46A22: Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10] 46B20: Geometry and structure of normed linear spaces 46B04: Isometric theory of Banach spaces 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 46E40: Spaces of vector- and operator-valued functions
Peralta, Antonio M. On the unit sphere of positive operators. Banach J. Math. Anal. 13 (2019), no. 1, 91--112. doi:10.1215/17358787-2018-0017. https://projecteuclid.org/euclid.bjma/1540865071