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Self-adjoint square roots of positive self-adjoint bounded linear operators

Published online by Cambridge University Press:  20 January 2009

C. A. Stuart
C. A. Stuart
Affiliation:
University of Sussex, Brighton
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A corollary of the main theorem presented in this note is a generalisation of the well-known result that a self-adjoint square root of a positive self-adjoint compact linear map in a Hilbert space is itself a compact linear map. The method used here exploits the techniques developed recently in the study of k-set contractions ((1), (2)).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 1 , June 1972 , pp. 77 - 79
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

(1) Nussbaum, R., The radius of the essential spectrum, Duke Math. J. 37 (1970), 473–478.CrossRefGoogle Scholar
(2) Webb, J. R. L., Remarks on k-set contractions, Boll. Un. Mat. Ital. (4) 4 (1971), 614–629.Google Scholar