Isometric flows in Hilbert space
- 1 January 1964
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 60 (1) , 45-49
- https://doi.org/10.1017/s0305004100037427
Abstract
1. Let {Vi}i≥0 be a weakly (hence also strongly) continuous semigroup of (linear) contraction operators on a Hilbert space H, i.e. |Vt| ≤ 1 ( t ≥ 0). Let Z and W denote the corresponding infinitesimal generator and cogenerator, i.e.Z is in general non-bounded, but closed and densely defined, and W is a contraction operator (everywhere defined in H), such that 1 is not a proper value of W. Conversely, every contraction operator W not having the proper value 1 is the infinitesimal cogenerator of exactly one semigroup {Vi} of the above type; one has namelyin the sense of the functional calculus for contraction operators (4).Keywords
This publication has 4 references indexed in Scilit:
- Shifts on Hilbert SpacesPublished by Springer Nature ,1983
- Isometric flows on Hilbert spaceBulletin of the American Mathematical Society, 1962
- Shifts on Hilbert spaces.Journal für die reine und angewandte Mathematik (Crelles Journal), 1961
- One-Parameter Semigroups of Isometric Operators in Hilbert SpaceAnnals of Mathematics, 1947