Hostname: page-component-84b7d79bbc-fnpn6 Total loading time: 0 Render date: 2024-07-28T20:11:41.337Z Has data issue: false hasContentIssue false

A simple proof of Arazy's theorem

Published online by Cambridge University Press:  20 January 2009

J. A. Erdos
Affiliation:
Department of MathematicsKing's CollegeLondon WC2R 2LS
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Arazy has characterized the isometries of p, (0 < p ≦ ∞, p ≠ 2) onto itself as all maps of the form XUXV where U and V are either both unitary or both anti-unitary. A simple proof of this result is given.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

1.Arazy, J., The isometries of p, Israel J. Math. 22 (1975), 247256.CrossRefGoogle Scholar
2.Anoussis, M. and Katavolos, A., p isometries of some operator algebras, preprint.Google Scholar
3.Gohberg, I. C. and Krein, M. G., Theory and Applications of Volterra Operators in Hilbert Space (Transl. Math. Monographs 24, Amer. Math. Soc, Providence, R.I., 1970).Google Scholar
4.McCarthy, C. A., p, Israel J. Math. 5 (1967), 249271.CrossRefGoogle Scholar
5.Sourour, A. R., Isometries of norm ideals of compact operators, J. Funct. Anal. 43 (1981), 6977.CrossRefGoogle Scholar