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A Note on Logarithms of Normal Operators

1962
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Proceedings of the American Mathematical Society
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All operators considered in this note are bounded and defined on a fixed Hubert space X. In [4] , C. R. Putnam has proved that if 77 is a positive definite selfadjoint operator and exp T = H, then ||f|| 2 In 2 implies that F is a selfadjoint operator. In Theorem 3 we prove that it is sufficient to assume that || T\\ <2ir in order that T be selfadjoint. This condition, already in the set of complex numbers, cannot be replaced by ||f|| ;£2ir without changing the conclusion. In Theorem 4 we prove

doi:10.2307/2034489
fatcat:jynhywurefft7nkbrmyww2xjhm