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On Square Roots and Logarithms of Self-Adjoint Operators

Published online by Cambridge University Press:  18 May 2009

C. R. Putnam
C. R. Putnam
Affiliation:
Purdue University Lafayette, Indiana, U.S.A.
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All operators considered in this paper are bounded and linear (everywhere defined) on a Hilbert space. An operator A will be called a square root of an operator B if

A simple sufficient condition guaranteeing that any solution A of (1) be normal whenever B is normal was obtained in [1], namely: If B is normal and if there exists some real angle θ for which Re(Aeιθ)≥0, then (1) implies that A is normal. Here, Re (C) denotes the real part ½(C + C*) of an operator C.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 1 , December 1958 , pp. 1 - 2
Copyright
Copyright © Glasgow Mathematical Journal Trust 1958

References

1.Putnam, C. R., On square roots of normal operators, Proc. Amer. Math. Soc., 8 (1957), 768–769.CrossRefGoogle Scholar
2.Wecken, F. J., Zur Theorie linearer Operatoren, Math. Annalen 110 (1935), 722–725.Google Scholar
3.Wintner, A., Ueber das Aequivalenzproblem beachrankter hermitescher Formen, Math. Z., 37 (1933), 254–263.CrossRefGoogle Scholar