Derivations on the algebra of measurable operators affiliated with a type I von Neumann algebra
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منابع مشابه
Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra
Let M be a type I von Neumann algebra with the center Z and a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M. We prove that any Z-linear derivation on L(M, τ) is inner and hence automatically continuous in the measure topology. If the lattice of projections from Z is atomic then any derivation on L(M, τ) is Z-linear. This implies...
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Let M be a type I von Neumann algebra with the center Z, a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M and let S0(M, τ) be the subalgebra in L(M, τ) consisting of all operators x such that given any ε > 0 there is a projection p ∈ P(M) with τ(p) < ∞, xp ∈ M and ‖xp‖ < ε. We prove that any Z-linear derivation of S0(M, τ) is spa...
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Given a von Neumann algebra M denote by S(M) and LS(M) respectively the algebras of all measurable and locally measurable operators affiliated with M. For a faithful normal semi-finite trace τ on M let S(M, τ) (resp. S0(M, τ)) be the algebra of all τ -measurable (resp. τ -compact) operators from S(M). We give a complete description of all derivations on the above algebras of operators in the ca...
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We construct a real valued dimension for arbitrary modules over the algebra of operators affiliated to a finite von Neumann algebra. Moreover we determine the algebraic K0and K1-group and the Lgroups of such an algebra.
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In this paper we generalize Brown’s spectral distribution measure to a large class of unbounded operators affiliated with a finite von Neumann algebra. Moreover, we compute the Brown measure of all unbounded R–diagonal operators in this class. As a particular case, we determine the Brown measure z = xy−1, where (x, y) is a circular system in the sense of Voiculescu, and we prove that for all n ...
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ژورنال
عنوان ژورنال: Siberian Advances in Mathematics
سال: 2008
ISSN: 1055-1344,1934-8126
DOI: 10.3103/s1055134408020028