Positive definiteness and commutativity of operators
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- by Jan Stochel PDF
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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.References
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Additional Information
- Jan Stochel
- Email: stochel@im.uj.edu.pl
- 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 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 431-440
- MSC (1991): Primary 47B20; Secondary 43A35
- DOI: https://doi.org/10.1090/S0002-9939-98-04075-1
- MathSciNet review: 1415340