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On joint essential spectra of doubly commuting n-tuples of p-hyponormal operators

Published online by Cambridge University Press:  18 May 2009

In Ho Jeon
In Ho Jeon
Affiliation:
Department of Mathematics, Sung Kyun Kwan University, Suwon 440–746, South Korea, E-mail: jih@math.skku.ac.kr
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Abstract

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Let A be an operator on a Hillbert space with polar decomposition A = |A|, let  = |A|½U|A|½ and let  = V|Â| be the polar decomposition of Â. Write à for the operatorà = |Â|½V|Â|½. If = (A1,…,AN) is a doubly commuting n-tuple of p-hyponormal operators on a Hillbert space with equal defect and nullity, then = (Ã1,…,Ãn) is a doubly commuting n-tuple of hyponormal operators. In this paper we show that

where σ* denotes σTe (Taylor essential spectrum), σTw (Taylor-Weyl spectrum) and σTb (Taylor-Browder spectrum), respectively.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 3 , September 1998 , pp. 353 - 358
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

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