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Products of positive operators

Published online by Cambridge University Press:  24 October 2008

S. J. Bernau
S. J. Bernau
Affiliation:
University of Texas, Austin, Texas 78712, U.S.A.
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Extract

Let H be a complex Hilbert space. Recall that a bounded linear operator A, on H, is positive if (Ax, x) ≥ 0 (x ∈ H) (so that A = A* necessarily) and positive definite if A is positive and invertible.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 2 , September 1974 , pp. 415 - 416
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Herstein, I. N. On a theorem of Wigner, Delta (Waukesha), 3 (1972/1973), 5–6.Google Scholar
(2)Kaplansky, IrvingLinear algebra and geometry (Allyn and Bacon; Boston, 1969).Google Scholar
(3)Kaplansky, IrvingTopological algebra. University of Chicago Mimeographed Lecture Notes, Chicago, III. (1952).Google Scholar
(4)Rickart, C. E.General Theory of Banach algebras (Von Nostrand; Princeton, 1960).Google Scholar
(5)Riesz, F. and Nagy, B.Sz. Functional analysis (Ungar; New York, 1966).Google Scholar
(6)Wigner, E. P.On weakly positive matrices. Canad. J. Math. 15 (1963), 313–318.CrossRefGoogle Scholar