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A simple proof of Arazy's theorem

Published online by Cambridge University Press:  20 January 2009

J. A. Erdos
J. A. Erdos
Affiliation:
Department of MathematicsKing's CollegeLondon WC2R 2LS
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Abstract

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

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 2 , June 1994 , pp. 239 - 242
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

1.Arazy, J., The isometries of p, Israel J. Math. 22 (1975), 247–256.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), 249–271.CrossRefGoogle Scholar
5.Sourour, A. R., Isometries of norm ideals of compact operators, J. Funct. Anal. 43 (1981), 69–77.CrossRefGoogle Scholar