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 | References | Similar Articles | Additional Information
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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- [2] F. H. Szafraniec, Note on a general dilation theorem, Ann. Polon. Math. (to appear). MR 529304 (80h:47008)
- [3] -, On the boundedness condition involved in dilation theory, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 877-881. MR 0425645 (54:13599)
- [4] B. Sz.-Nagy, Extensions of linear transformations in Hilbert space which extend beyond this space, Appendix to F. Riesz, B. Sz.-Nagy, Functional Analysis, Ungar, New York, 1960.
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-, Products of operators of classes
, Rev. Roumaine Math. Pures Appl. 13 (1968), 897-899. MR 0239455 (39:812)
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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
