The Tensor Product Formula for Reflexive Subspace Lattices
Canadian mathematical bulletin, Tome 38 (1995) no. 3, pp. 308-316

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1995-045-x
Mots-clés : 47A15
Harrison, K. J. The Tensor Product Formula for Reflexive Subspace Lattices. Canadian mathematical bulletin, Tome 38 (1995) no. 3, pp. 308-316. doi: 10.4153/CMB-1995-045-x
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[1] 1. Arveson, W., Operator algebras and invariant subspaces, Ann. of Math. 100(1974), 433–532. Google Scholar

[2] 2. Davidson, K., Nest Algebras, Pitman Res. Notes Math. 191, Longman Sci. Tech, 1988. Google Scholar

[3] 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] 4. Hopenwasser, A., Tensor products of reflexive subspace lattices, Michigan Math. J. 29(1984), 359–370. Google Scholar

[5] 5. Hopenwasser, A. and Kraus, J., Tensor products of reflexive algebras II, J. London Math. Soc. 28(1983), 359–362. Google Scholar

[6] 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] 7. Kraus, J., W*-dynamical systems and reflexive operator algebras, J. Operator Theory 8(1982), 181–194. Google Scholar

[8] 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] 9. Kraus, J., Tensor products of reflexive algebras, J. London Math. Soc. 28(1983), 350–358. Google Scholar

[10] 10. Kraus, J., The slice map problem and approximation properties, J. Funct. Anal. 102(1991), 116–155. Google Scholar

[11] 11. Longstaff, W. E., Strongly reflexive lattices, J. London Math. Soc. 11(1975), 491–498. Google Scholar

[12] 12. Raney, G. N., Completely distributive complete lattices, Proc. Amer. Math. Soc. 3(1952), 677–680. Google Scholar

[13] 13. Raney, G. N., A subdirect union representation of completely distributive complete lattices, Proc. Amer. Math. Soc. 4(1953), 514–522. Google Scholar

[14] 14. Raney, G. N., Tight Galois connections and complete distributivity, Trans. Amer. Math. Soc. 97(1960), 418–426. Google Scholar

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