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On Decomposability of Compact Perturbations of Normal Operators

Published online by Cambridge University Press:  20 November 2018

M. Radjabalipour  and
H. Radjavi
M. Radjabalipour
Affiliation:
Dalhousie University, Halifax, Nova Scotia
H. Radjavi
Affiliation:
Dalhousie University, Halifax, Nova Scotia
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The main purpose of this paper is to show that a bounded Hilbert-space operator whose imaginary part is in the Schatten class Cp(1 ≦ p < ∞ ) is strongly decomposable. This answers affirmatively a question raised by Colojoara and Foias [6, Section 5(e), p. 218].

In case 0 ≦ T* — T ∈ C1, it was shown by B. Sz.-Nagy and C. Foias [2, p. 442; 25, p. 337] that T has many properties analogous to those of a decomposable operator and by A. Jafarian [11] that T is strongly decomposable. The authors of [11] and [24] employ the properties of the characteristic function of the contraction operator obtained from the Cayley transform of T;

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 725 - 735
Copyright
Copyright © Canadian Mathematical Society 1975

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