Proceedings of the American Mathematical Society

Author(s): Jan Stochel
Journal: Proc. Amer. Math. Soc. 126 (1998), 431-440.
MSC (1991): Primary 47B20; Secondary 43A35
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47B20, 43A35

Jan Stochel
Affiliation: Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, PL-30059 Kraków, Poland
Email: stochel@im.uj.edu.pl

DOI: 10.1090/S0002-9939-98-04075-1
PII: S 0002-9939(98)04075-1
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
Copyright of article: Copyright 1998, American Mathematical Society

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