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One-parameter automorphism groups of operator algebras allowing spectral projections

Published online by Cambridge University Press:  19 September 2008

George A. Elliott  and
László Zsidó
George A. Elliott
Affiliation:
Mathematics Institute, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark;
László Zsidó
Affiliation:
Mathematisches Institut A, Pfaffenwaldring 57, D-7000 Stuttgart 80, West Germany
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Abstract

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The property of a one-parameter C*- (or W*-) dynamical system that the spectral subspaces corresponding to the three subsets (−∞, 0), {0}, and (0, +∞) add up to the whole algebra is reformulated. If the C*-algebra is prime (or the W*-algebra is a factor), an equivalent property is that the spectrum is finite.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 2 , June 1984 , pp. 187 - 212
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Arveson, W.. On groups of automorphisms of operator algebras. J. Funct. Anal. 15 (1974), 217–243.CrossRefGoogle Scholar
[2]Cioraˇnescu, I. & Zsidó, L.. Analytic generators for one-parameter groups. Tôhoku Math. J. 28 (1976), 327–362.Google Scholar
[3]Cioraˇnescu, I. & Zsidó, L.. On spectral subspaces of some unbounded groups of operators. Rev. Roumaine Math. Pures Appl. 21 (1976), 817–850.Google Scholar
[4]Combes, F. & Delaroche, C.. Représentations des groupes localement compacts et applications aux algèbres d'opérateurs. Astérisque 55 (1978).Google Scholar
[5]Elliott, G. A. & Zsidó, L.. Almost uniformly continuous automorphism groups of operator algebras. J. Operator Theory 8 (1982), 227–277.Google Scholar
[6]Glimm, J. G.. A Stone-Weierstrass theorem for C *-algebras, Ann. of Math. 72 (1960), 216–244.CrossRefGoogle Scholar
[7]Greenleaf, F. P.. Invariant Means on Topological Groups and their Applications. Van Nostrand-Reinhold: New York, 1969.Google Scholar
[8]Halpern, H.. Irreducible module homomorphisms of a von Neumann algebra into its center. Trans. Amer. Math. Soc. 140 (1969), 195–221.CrossRefGoogle Scholar
[9]Hille, E. & Phillips, R. S.. Functional Analysis and Semigroups. American Mathematical Society: Providence, Rhode Island, 1957.Google Scholar
[10]Kadets, M. J. & Mityagin, B. S.. Complemented subspaces in Banach spaces. Uspekhi Mat. Nauk 28, No. 6 (1973), 77–94.Google Scholar
[11]Olesen, D.. On spectral subspaces and their applications to automorphism groups. In Symposia Mathematica Vol. XX, pp. 253–296. Academic Press: London, 1976.Google Scholar
[12]Pedersen, G. K.. C*-algebras and their Automorphism Groups. Academic Press: London, 1979.Google Scholar
[13]Riesz, F. & Nagy, B. Sz.. Lecons d'Analyse Fonctionelle, 3e édition. Akadémiai Kiadó: Budapest, 1955.Google Scholar
[14]Rudin, W.. Projection on invariant subspaces. Proc. Amer. Math. Soc. 13 (1962), 429–432.CrossRefGoogle Scholar
[15]Sakai, S.. C*-algebras and W*-algebras. Springer-Verlag: New York, 1971.Google Scholar
[16]Zsidó, L.. Spectral and ergodic properties of the analytic generator. J. Approx. Theory 20 (1977), 77–138.CrossRefGoogle Scholar
[17]Zsidó, L.. On spectral subspaces associated to locally compact abelian groups. Advances in Math. 36 (1980), 213–276.Google Scholar
[18]Zsidó, L.. Spectral properties of the analytic generator and singular integrals. Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8) 17 (1983), 105–134.Google Scholar