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Bures distance function and a generalization o f Sakai’s non-commutative Radon-Nikodym theorem. (English) Zbl 0252.46075


MSC:

46L10 General theory of von Neumann algebras
46K10 Representations of topological algebras with involution
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[1] Araki, H., Publ. RIMS Kyoto Univ. 6 (1970/71), 477-487.
[2] Bures, D.J.C., Trans. Amer. Math. Soc. 135 (1969), 199-212
[3] Dixmier, J., Les Algebres d’Operateurs dans VEspace Hilbertien, 2nd ed., Gauthier Villars, Paris, 1969.
[4] Dye, H.A., Trans. Amer. Math. Soc. 70 (1952), 243-280.
[5] Sakai, S., Bull. Amer. Math. Soc. 71 (1965), 149-151.
[6] Sakai, S., C*-Algebras and W*-Algebras, Springer-Verlag, New York, Heidelberg, Berlin, 1971.
[7] Segal, I.E., Ann. of Math. 57 (1953), 401-457. · Zbl 0051.34201
[8] Takesaki, M., Tomita’s Theory of Modular Hilbert Algebras and Its Applications, Springer-Verlag, Berlin, Heidelberg, New York, 1970. Note Added in Proof. Professor J. Dixmier has pointed out that 1-E in Lemma 4 is the support of the normal state (3F3 Q@) and hence its existence is well-known. · Zbl 0193.42502
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