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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
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?)

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  • [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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Keywords: Positive definiteness, boundedness condition, Sz.-Nagy's dilation theorem, the Bram-Halmos criterion
Article copyright: © Copyright 1977 American Mathematical Society

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