Comparison of Commuting One-Parameter Groups of Isometries

Ola Bratteli, Hideki Kurose, Derek W. Robinson
1990 Transactions of the American Mathematical Society  
Let a , ß be two commuting strongly continuous one-parameter groups of isometries on a Banach space j/ with generators <5Q and <5" , and analytic elements srff , srff , respectively. Then it is easy to show that if ôa is relatively bounded by <5» , then srff Ç sAf , and in this paper we establish the inverse implication for unitary one-parameter groups on Hubert spaces and for one-parameter groups of '-automorphisms of abelian C*-algebras. It is not known in general whether the inverse
more » ... he inverse implication holds or not, but it does not hold for one-parameter semigroups of contractions.
doi:10.2307/2001696 fatcat:g6u6tw7cb5cqznc2iluyojzviq