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Diagonals of nilpotent operators

Published online by Cambridge University Press:  20 January 2009

C. K. Fong
C. K. Fong
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada, M5S 1A1
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The purpose of the present note is to answer the following question of T. A. Gillespie,learned from G. J. Murphy [4]: for which sequences{an} of complex numbers does there exist a quasinilpotent operator Q on a (separable, infinite-dimensional, complex) Hilbert space H, which has{an} as a diagonal, that is (Qen,en)=n for some orthonormal basis{en} in H?

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 2 , June 1986 , pp. 221 - 224
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

REFERENCES

1Fan, Peng, On the diagonal of an operator, Trans. Amer. Math. Soc. 283 (1984), 239–251.CrossRefGoogle Scholar
2Fan, Peng and Fong, Che-Kao, Operators with zero diagonals.Google Scholar
3Fillmore, P. A., On similarity and the diagonal of an matrix, Amer. Math. Monthly 76 (1969), 167–169.CrossRefGoogle Scholar
4Murphy, G. J., Private communication, (1983).Google Scholar