Comparison of commuting one-parameter groups of isometries

Authors:
Ola Bratteli, Hideki Kurose and Derek W. Robinson

Journal:
Trans. Amer. Math. Soc. **320** (1990), 677-694

MSC:
Primary 47D03; Secondary 46L40, 46L57

DOI:
https://doi.org/10.1090/S0002-9947-1990-0968886-8

MathSciNet review:
968886

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Abstract: Let be two commuting strongly continuous one-parameter groups of isometries on a Banach space with generators and , and analytic elements , respectively. Then it is easy to show that if is relatively bounded by , then , and in this paper we establish the inverse implication for unitary one-parameter groups on Hilbert spaces and for one-parameter groups of -automorphisms of abelian -algebras. It is not known in general whether the inverse implication holds or not, but it does not hold for one-parameter semigroups of contractions.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1990-0968886-8

Article copyright:
© Copyright 1990
American Mathematical Society