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The Tomita Decomposition of Rings of Operators

1964
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Transactions of the American Mathematical Society
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i) I. Introduction. It is known that if R is a symmetric ring of bounded operators on a separable Hubert space H and f 0 is a vector in H which is cyclic with respect to R, then the positive functional F(A)= (AÇ0, £0), for A e R, may be written as a direct integral over a compact Hausdorff space M, i.e., F(A) = ¡Mfm(A)dp(m) where p is a positive regular Borel measure and the functionals fm are indecomposable except, at most, for m eM0 <= M and p(M0) -0. This decomposition of F induces a

doi:10.2307/1994089
fatcat:snq25yvntrgdjniyuoiuxmv42e