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Real parts of quasi-nilpotent operators

Published online by Cambridge University Press:  20 January 2009

P. A. Fillmore ,
C. K. Fong  and
A. R. Sourour
P. A. Fillmore
Affiliation:
Dalhousie University, Halifax, Nova Scotia
C. K. Fong
Affiliation:
Dalhousie University, Halifax, Nova Scotia
A. R. Sourour
Affiliation:
University of Toronto, Toronto, Ontario
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The purpose of this paper is to answer the question: which self-adjoint operators on a separable Hilbert space are the real parts of quasi-nilpotent operators? In the finite-dimensional case the answer is: self-adjoint operators with trace zero. In the infinite dimensional case, we show that a self-adjoint operator is the real part of a quasi-nilpotent operator if and only if the convex hull of its essential spectrum contains zero. We begin by considering the finite dimensional case.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 3 , October 1979 , pp. 263 - 269
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

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