Nihonkai Mathematical Journal

Maps on the sphere of the algebras of matrices

Osamu Hatori

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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.

Article information

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

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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

Isometry sphere algebra of matrices unitarily invariant norm strictly convex norm


Hatori, Osamu. Maps on the sphere of the algebras of matrices. Nihonkai Math. J. 26 (2015), no. 2, 121--125.

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