Bundle convergence in a von Neumann algebra and in a von Neumann subalgebra

• Autorzy: Le Gac B. , Moricz F.
• Języki publikacji: EN

Abstrakty

EN

Let H be a separable complex Hilbert space, A a von Neumann algebra in L(H), [phi] a faithful, normal state on A, and B a commutative von Neumann subalgebra of A. Given a sequence (X[n] : n is less than or equal to 1) of operators in B, we examine the relations between bundle convergence in B and bundle convergence in A.

Słowa kluczowe

EN

von Neumann algebra and subalgebra; faithful and normal state; bundle convergence; almost uniform convergence; conditional expectation in a von Neumann algebra

PL

algebra von Neumanna; podalgebra von Neumanna; stan wierny i normalny; zbieżność wiązki; zbieżność prawie jednostajna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 3
• Strony: 283--295
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Le Gac B.

• Université de Provence, Centre de Mathématiques et Informatique, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France

autor

Moricz F.

• Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary

Bibliografia

• [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann), deuxième édition, Gauthier-Villars, Paris, 1969.
• [2] E. Hensz, R. Jajte and A. Paszkiewicz, The bundle convergence in von Neumann algebras and their L2-spaces, Studia Math. 120 (1996), 23-46.
• [3] R. Jajte, Strong Limit Theorems in Noncommutative Probability, Lecture Notes In Math. 1110, Springer, Berlin, 1985.
• [4] -, Strong Limit Theorems in Noncommutative L2-Spaces, Lecture Notes in Math. 1477, Springer, Berlin, 1991.
• [5] B. Le Gac and F. Móricz, Beppo Levi and Lebesgue type theorems for bundle convergence in noncommutative L2-spaces, in: Oper. Theory Adv. Appl. 127, Birkhäuser, Basel, 2001, 447-464.
• [6] A. Paszkiewicz, Convergence in W*-algebras, J. Funct. Anal. 69 (1986), 143-154.
• [7] M. Takesaki, Theory of Operator Algebras II, Encyclopaedia Math. Sci. 125, Springer, Berlin, 2003.