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Proceedings of the American Mathematical Society

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Dilations on involution semigroups


Author: F. H. Szafraniec
Journal: Proc. Amer. Math. Soc. 66 (1977), 30-32
MSC: Primary 47A20; Secondary 47B20
DOI: https://doi.org/10.1090/S0002-9939-1977-0473873-1
MathSciNet review: 0473873
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Abstract: We present an equivalent form of the boundedness condition involved in the Sz.-Nagy general dilation theorem and, as a consequence, we prove a dilation theorem for a product of commuting dilatable operator functions on involution semigroups. Also we show that the Bram-Halmos criterion of subnormality can be directly deduced from the proposed boundedness condition.


References [Enhancements On Off] (What's this?)

  • [1] Joseph Bram, Subnormal operators, Duke Math. J. 22 (1955), 75–94. MR 0068129
  • [2] F. H. Szafraniec, Note on a general dilation theorem, Ann. Polon. Math. 36 (1979), no. 1, 43–47. MR 529304
  • [3] F. H. Szafraniec, On the boundedness condition involved in dilation theory, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), no. 10, 877–881 (English, with Russian summary). MR 0425645
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0473873-1
Keywords: Positive definiteness, boundedness condition, Sz.-Nagy's dilation theorem, the Bram-Halmos criterion
Article copyright: © Copyright 1977 American Mathematical Society