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The Relationship Between Distance Formulae and Compact Perturbations for Reflexive Algebras

Published online by Cambridge University Press:  20 November 2018

Kenneth R. Davidson
Kenneth R. Davidson*
Affiliation:
Pure Mathematics Department University of Waterloo Waterloo, Ontario, N2L 3G1
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Abstract

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For completely distributive CSL algebras, hyper-reflexivity is equivalent to a description of the compact perturbation of the algebra analogous to the Fall-Arveson-Muhly Theorem for nest algebras.

Keywords

47D25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 4 , 01 December 1990 , pp. 489 - 493
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Andersen, N. T., Compact perturbations of reflexive algebras, J. Func. Anal. 38 (1980) 366–400.Google Scholar
2. Arveson, W. B., Interpolation problems in nest algebras, J. Func. Anal. 20 (1975), 208–233.Google Scholar
3. Arveson, W. B., Perturbation theory for groups and lattices, J. Func. Anal. 53 (1983), 22–73.Google Scholar
4. Christensen, E., Perturbations of operator algebras II, Indiana Univ. Math. J. 26 (1977) 891–904.Google Scholar
5. Davidson, K. R., Similarity and compact perturbations of nest algebras, J. Reine Angew. Math, 348 (1984), 286–294.Google Scholar
6. Davidson, K. R., Nest Algebras, Longman Scientific Pitman Research Notes in Math., 191, Essex, 1988.Google Scholar
7. Davidson, K. R., and D.R. Pitts, Complete distributivity and compactness of commutative subspace lattices, J. London Math. Soc, (to appear).Google Scholar
8. Davidson, K. R., and Power, S.C., Failure of the distance formula, J. London Math. Soc. (2) 32 (1984) 157–165.Google Scholar
9. Davidson, K. R., and Power, S.C., Best approximation in C*-algebras, J. reine angew. Math. 368 (1986) 43–62.Google Scholar
10. Fall, T., Arveson, W. B., Muhly, P., Perturbations of nest algebras, J. Operator Theory 1 (1976), 137— 150.Google Scholar
11. Froelich, J., Compact operators, invariant subspaces, and spectral synthesis, Ph.D. Thesis, Univ. Iowa, 1984.Google Scholar
12. Gilfeather, F., Hopenwasser, A., Larson, D., Reflexive algebras with finite width lattices: tensor products, cohomology, compact perturbations, J. Func. Anal. 55 (1984), 176–199.Google Scholar
13. Hopenwasser, A., Laurie, C., Moore, R., Reflexive algebras with completely distributive subspace lattices, J. Operator Theory 11 (1984) 91–108.Google Scholar
14. Larson, D. R., Nest algebras and similarity transformations, Ann. Math. 121 (1985) 409–427.Google Scholar
15. Laurie, C., Longstaff, W., A note on rank one operators in reflexive algebras, Proc, Amer. Math. Soc. 89(1983), 293–297.Google Scholar
16. Rosenoer, S., Distance estimates for von Neumann algebras, Proc. Amer. Math. Soc. 86 (1982), 248– 252.Google Scholar
17. Voiculescu, D., A non-commutative Weyl von Neumann theorem, Rev. Roum. Math. Pures et Appl. 21 (1976) 97–113.Google Scholar
18. Wagner, B., Weak limits of projections and compactness ofsubspace lattices, Trans. Amer. Math. Soc. 304(1987), 515–535.Google Scholar