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A remark on the essential spectra of quasi-similar dominant contractions

Published online by Cambridge University Press:  18 May 2009

B. P. Duggal
B. P. Duggal
Affiliation:
School of Mathematical Sciences, University of Khartoum, P.O. Box 321, Khartoum, Sudan
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We consider operators, i.e. bounded linear transformations, on an infinite dimensional separable complex Hilbert space H into itself. The operator A is said to be dominant if for each complex number λ there exists a number Mλ(≥l) such that ∥(A – λ)*x∥ ≤ Mλ∥A – λ)x∥ for each x∈H. If there exists a number M≥Mλ for all λ, then the dominant operator A is said to be M-hyponormal. The class of dominant (and JW-hyponormal) operators was introduced by J. G. Stampfli during the seventies, and has since been considered in a number of papers, amongst then [7], [11]. It is clear that a 1-hyponormal is hyponormal. The operator A*A is said to be quasi-normal if Acommutes with A*A, and we say that A is subnormal if A has a normal extension. It is known that the classes consisting of these operators satisfy the following strict inclusion relation:

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 2 , May 1989 , pp. 165 - 168
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

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