Invariant subspaces of von Neumann algebras. II

Peligrad, Costel

doi:10.1090/S0002-9939-1979-0518517-7

Invariant subspaces of von Neumann algebras. II
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Proc. Amer. Math. Soc. 73 (1979), 346-350 Request permission

Abstract:

It is shown that every parareductive operator algebra $A \subset B(H)$ (as defined below) is a von Neumann algebra. For the proof of this result, some new properties of paraclosed operators are obtained. Finally, a sufficient condition that a reductive algebra be a von Neumann algebra is given.

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C. Peligrad, Invariant subspaces of von Neumann algebras, Acta Sci. Math. (Szeged) 37 (1975), no. 3-4, 273–277. MR 394234
Heydar Radjavi and Peter Rosenthal, Invariant subspaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 77, Springer-Verlag, New York-Heidelberg, 1973. MR 0367682
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