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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Positive definiteness
and commutativity of operators

Author: Jan Stochel
Journal: Proc. Amer. Math. Soc. 126 (1998), 431-440
MSC (1991): Primary 47B20; Secondary 43A35
MathSciNet review: 1415340
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Abstract: It is shown that an $n$-tuple of bounded linear operators on a complex Hilbert space, which is positive definite in the sense of Halmos, must be commutative. Some generalizations of this result to the case of pairs of unbounded operators are obtained.

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Jan Stochel

Keywords: Formally normal operator, normal operator, subnormal operator, commutativity, positive definiteness
Received by editor(s): July 29, 1996
Additional Notes: This work was supported by a grant of the Komitet Bada Naukowych, Warsaw.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society