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Sums and products of quasi-nilpotent operators

Published online by Cambridge University Press:  14 November 2011

C. K. Fong  and
A. R. Sourour
C. K. Fong
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada
A. R. Sourour
Affiliation:
Department of Mathematics, University of Victoria, Victoria, British Columbia V8W 2Y2, Canada
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Extract

It is proved that a bounded operator on Hilbert space is the sum of two quasi-nilpotent operators if and only if it is not a non-zero scalar plus a compact operator. Necessary conditions and sufficient conditions for an operator to be the product of two quasi-nilpotent operators are given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 1-2 , 1984 , pp. 193 - 200
Copyright
Copyright © Royal Society of Edinburgh 1984

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