Nihonkai Mathematical Journal
- Nihonkai Math. J.
- Volume 26, Number 2 (2015), 121-125.
Maps on the sphere of the algebras of matrices
Let $S_n$ be the unit sphere with respect to the operator norm of the algebra of $n\times n$ complex matrices. We give a complete description of the form of surjections on $S_n$ which preserve the metric induced by a unitarily invariant strictly convex norm.
Nihonkai Math. J., Volume 26, Number 2 (2015), 121-125.
Received: 27 October 2015
Revised: 5 November 2015
First available in Project Euclid: 12 July 2016
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]
Secondary: 15A86: Linear preserver problems 46B04: Isometric theory of Banach spaces
Hatori, Osamu. Maps on the sphere of the algebras of matrices. Nihonkai Math. J. 26 (2015), no. 2, 121--125. https://projecteuclid.org/euclid.nihmj/1468334492