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On the structure of polynomially normal operators

Published online by Cambridge University Press:  17 April 2009

Fuad Kittaneh
Fuad Kittaneh
Affiliation:
Department of Mathematics, United Arab Emirates University, PO Box 15551, Al-Ain, United Arab Emirates
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Abstract

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We present some results concerning the structure of polynomially normal operators. It is shown, among other things, that if Tn is normal for some n > 1, then T is quasi–similar to a direct sum of a normal operator and a compact operator and if p(T) is normal with T essentially normal, then T can be written as the sum of a normal operator and a compact operator. Utilizing the direct integral theory of operators we finally show that if p(T) is normal and T*T commutes with T + T*, then T must be normal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 1 , August 1984 , pp. 11 - 18
Copyright
Copyright © Australian Mathematical Society 1984

References

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