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Free E 0-Semigroups

Published online by Cambridge University Press:  20 November 2018

Neal J. Fowler
Neal J. Fowler*
Affiliation:
University of Calgary, Calgary, Alberta
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Abstract

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Given a strongly continuous semigroup of isometries ∪ acting on a Hilbert space ℋ, we construct an E 0-semigroup α∪ , the free E 0-semigroup over ∪, acting on the algebra of all bounded linear operators on full Fock space over ℋ. We show how the semigroup αU⊗V can be regarded as the free product of α∪ and αV. In the case where U is pure of multiplicity n, the semigroup au, called the Free flow of rank n, is shown to be completely spatial with Arveson index +∞. We conclude that each of the free flows is cocycle conjugate to the CAR/CCR flow of rank +∞.

Keywords

46L4081E05

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 4 , 01 August 1995, pp. 744 - 785
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Arveson, W., Quantizing the Fredholm index, Proceedings of the Great Plains Operator Theory Seminar, 1988.Google Scholar
2. Arveson, W., An addition formula for the index of semigroups ofendomorphisms of ℬ (ℋ), Pacific J. Math. (1) 137(1989), 19–36.Google Scholar
3. Arveson, W., Continuous analogues of Fock space, Mem. Amer. Math. Soc. (409) 80(1989).Google Scholar
4. Cuntz, J., Simple C*-algebras generated by isometries, Comm. Math. Phys. 57(1977), 173–185.Google Scholar
5. Dykema, K.J., Voiculescu, D.V. and Nica, A., Free Random Variables, CRM Monograph Series, Amer. Math. Soc., Providence, Rhode Island, 1992.Google Scholar
6. Evans, D., On On, Publ. Res. Inst. Math. Sci. 16(1980), 915–927.Google Scholar
7. Hugenholtz, N.M. and Kadison, R.V., Automorphisms and quasi-free states of the CAR algebra, Comm. Math. Phys. 43(1975), 181–197.’Google Scholar
8. Powers, R., A non-spatial continuous semigroup of *-endomorphisms of ℬ (ℋ), Publ. Res. Inst. Math. Sci. 23(1987), 1053–1069.Google Scholar
9. Powers, R., An index theory for semigroups of *-endomorphisms of ℬ (ℋ) and type ll\ factors, Canad. J. Math. (1) 40(1988), 86–114.Google Scholar
10. Powers, R. and Robinson, D., An index for continuous semigroups of *-endomorphisms of ℬ (ℋ), J. Funct. Anal. 84(1989), 85–96.Google Scholar
11. Roberts, J.E., Cross Products of von Neumann algebras by group duals, Sympos. Math., Instituto Nazionale di alta Matematica, Academic Press, London, 1976.Google Scholar