Innerness of derivations on subalgebras of measurable operators
نویسندگان
چکیده
منابع مشابه
Local Derivations on Algebras of Measurable Operators
The paper is devoted to local derivations on the algebra S(M, τ) of τ measurable operators affiliated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every local derivation on S(M, τ) which is continuous in the measure topology, is in fact a derivation. In the particular case of type I von Neumann algebras they all are inner derivations. It is proved that f...
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نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولInnerness of ρ-derivations on Hyperfinite Von Neumann Algebras
Suppose that M,N are von Neumann algebras acting on a Hilbert space and M is hyperfinite. Let ρ : M → N be an ultraweakly continuous ∗-homomorphism and let δ : M → N be a ∗-ρ-derivation such that δ(I) commutes with ρ(I). We prove that there is an element U in N with ‖U‖ ≤ ‖δ‖ such that δ(A) = Uρ(A)− ρ(A)U for all A ∈ M. c © Electronic Journal of Theoretical Physics. All rights reserved.
متن کاملStructure of derivations on various algebras of measurable operators for type I von Neumann algebras
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...
متن کاملDerivations 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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ژورنال
عنوان ژورنال: Lobachevskii Journal of Mathematics
سال: 2008
ISSN: 1995-0802,1818-9962
DOI: 10.1134/s1995080208020030