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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0473873-1
PII: S 0002-9939(1977)0473873-1
Keywords: Positive definiteness, boundedness condition, Sz.-Nagy's dilation theorem, the Bram-Halmos criterion
Article copyright: © Copyright 1977 American Mathematical Society