Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T04:21:18.897Z Has data issue: false hasContentIssue false
  • English
  • Français

The Tensor Product Formula for Reflexive Subspace Lattices

Published online by Cambridge University Press:  20 November 2018

K. J. Harrison
K. J. Harrison*
Affiliation:
School of Mathematical and Physical Sciences, Murdoch University, Australia, e-mail:[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a characterisation of where and are subspace lattices with commutative and either completely distributive or complemented. We use it to show that Lat is a CSL algebra with a completely distributive or complemented lattice and is any operator algebra.

Keywords

47A15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 3 , 01 September 1995 , pp. 308 - 316
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Arveson, W., Operator algebras and invariant subspaces, Ann. of Math. 100(1974), 433–532.Google Scholar
2. Davidson, K., Nest Algebras, Pitman Res. Notes Math. 191, Longman Sci. Tech, 1988.Google Scholar
3. Gilfeather, F., Hopenwasser, A. and Larson, D., Reflexive algebras with finite width lattices: tensor products, cohomology, compact perturbations, J. Funct. Anal. 55(1984), 176–199.Google Scholar
4. Hopenwasser, A., Tensor products of reflexive subspace lattices, Michigan Math. J. 29(1984), 359–370.Google Scholar
5. Hopenwasser, A. and Kraus, J., Tensor products of reflexive algebras II, J. London Math. Soc. 28(1983), 359–362.Google Scholar
6. Hopenwasser, A., Laurie, C. and Moore, R., Reflexive algebras with completely distributive subspace lattices, J. Operator Theory 11(1984), 91–108.Google Scholar
7. Kraus, J., W*-dynamical systems and reflexive operator algebras, J. Operator Theory 8(1982), 181–194.Google Scholar
8. Kraus, J., The slice map problem for σ-weakly closed subspaces onf von Neumann algebras, Trans. Amer. Math. Soc. 279(1983), 357–376.Google Scholar
9. Kraus, J., Tensor products of reflexive algebras, J. London Math. Soc. 28(1983), 350–358.Google Scholar
10. Kraus, J., The slice map problem and approximation properties, J. Funct. Anal. 102(1991), 116–155.Google Scholar
11. Longstaff, W. E., Strongly reflexive lattices, J. London Math. Soc. 11(1975), 491–498.Google Scholar
12. Raney, G. N., Completely distributive complete lattices, Proc. Amer. Math. Soc. 3(1952), 677–680.Google Scholar
13. Raney, G. N., A subdirect union representation of completely distributive complete lattices, Proc. Amer. Math. Soc. 4(1953), 514–522.Google Scholar
14. Raney, G. N., Tight Galois connections and complete distributivity, Trans. Amer. Math. Soc. 97(1960), 418–426.Google Scholar