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On homomorphisms of an orthogonally decomposable Hilbert space, III

  • Fumio Hiai (a1) and Sadayuki Yamamuro (a2)

Abstract

A hyperfinite von Neumann algebra satisfies the condition that every o.d. homomorphism is a normal operator if and only if it is a factor of type In.

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References

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[1]Ando, T., ‘Operators with a norm condition’, Acta Sci. Math. (Szeged) 33 (1972), 169178.
[2]Bratteli, O. and Robinson, D. W., Operator algebras and quantum statistical mechanics I, (Springer-Verlag, Berlin-Heidelberg-New York, 1979).
[3]Connes, A., ‘Caractérisation des espaces vectoriels ordonnés sous-jacents aux algébres de von Neumann’, Ann. Inst. Fourier, (Grenoble), 24 (1974), 121155.
[4]Connes, A, ‘Classification of injective factors, cases II1, II, IIIλ, λ ≠ 1’, Ann. of Math. 104 (1976), 73115.
[5]Dang, T. B. and Yamamuro, S., ‘On homomorphisms of an orthogonally decomposable Hilbert space’, J. Functional Analysis 68 (1986), 366373.
[6]Dixmier, J., Les algèbres d'opérateurs dan l'espaces hilbertien (Algèbres de von Neumann) (Gauthier-Villars, Paris, 1957).
[7]Kadison, R. V., ‘A generalized Schwarz inequality and algebraic invariants for operator algebras’, Ann. of Math. 56 (1952), 494503.
[8]Yamamuro, S., ‘Absolute values in orthogonally decomposable spaces’, Bull. Austral. Math. Soc. 31 (1985), 215233.
[9]Yamamuro, S., ‘On homomorphisms of an orthogonally decomposable Hilbert space II’, J. Austral. Math. Soc., to appear.
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On homomorphisms of an orthogonally decomposable Hilbert space, III

  • Fumio Hiai (a1) and Sadayuki Yamamuro (a2)

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