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On the commutants modulo Cp of A2 and A3

Published online by Cambridge University Press:  09 April 2009

Fuad Kittaneh
Fuad Kittaneh
Affiliation:
Department of Mathematics, United Arab Emirates University, P. O. Box 15551 A1-Ain, U.A.E.
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Abstract

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We prove the following statements about bounded linear operators on a complex separable infinite dimensional Hilbert space. (1) Let A and B* be subnormal operators. If A2X = XB2 and A3X = XB3 for some operator X, then AX = XB. (2) Let A and B* be subnormal operators. If A2X – XB2 ∈ Cp and A3X – XB3 ∈ Cp for some operator X, then AX − XB ∈ C8p. (3) Let T be an operator such that 1 − T*T ∈ Cp for some p ≥1. If T2X − XT2 ∈ Cp and T3X – XT3 ∈ Cp for some operator X, then TX − XT ∈ Cp. (4) Let T be a semi-Fredholm operator with ind T < 0. If T2X − XT2 ∈ C2 and T3X − XT3 ∈ C2 for some operator X, then TX − XT ∈ C2.

Keywords

commutantnormal operatorssubnormal operatorsisometrySchatten p-class
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 1 , August 1986 , pp. 47 - 50
Copyright
Copyright © Australian Mathematical Society 1986

References

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