Dilations on involution semigroups
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- by F. H. Szafraniec PDF
- Proc. Amer. Math. Soc. 66 (1977), 30-32 Request permission
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
- Joseph Bram, Subnormal operators, Duke Math. J. 22 (1955), 75–94. MR 68129
- F. H. Szafraniec, Note on a general dilation theorem, Ann. Polon. Math. 36 (1979), no. 1, 43–47. MR 529304, DOI 10.4064/ap-36-1-43-47
- 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 425645 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.
- Béla Sz.-Nagy, Products of operators of classes $C_{\rho }$, Rev. Roumaine Math. Pures Appl. 13 (1968), 897–899. MR 239455
Additional Information
- © Copyright 1977 American Mathematical Society
- 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