Nihonkai Mathematical Journal

Maps on the sphere of the algebras of matrices

Osamu Hatori

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Abstract

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

Source
Nihonkai Math. J., Volume 26, Number 2 (2015), 121-125.

Dates
Received: 27 October 2015
Revised: 5 November 2015
First available in Project Euclid: 12 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1468334492

Mathematical Reviews number (MathSciNet)
MR3521506

Zentralblatt MATH identifier
1361.15029

Subjects
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

Keywords
Isometry sphere algebra of matrices unitarily invariant norm strictly convex norm

Citation

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


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References

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