$$L_1$$ L 1 -space for a positive operator affiliated with von Neumann algebra
نویسندگان
چکیده
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...
متن کاملDerivations on the Algebra of τ-Compact Operators Affiliated with a Type I von Neumann Algebra
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...
متن کاملOn the K- and L-theory of the Algebra of Operators Affiliated to a Finite Von Neumann Algebra
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.
متن کاملBrown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra
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 ...
متن کاملA Counterexample in Von Neumann Algebra Dynamics
In this essay we construct a noncommutative von Neumann dynamical system with certain pathological properties from the viewpoint of analogies with classical ergodic theory. These relate to obstructions to the existence of special kinds of subsystem or subextension. We will build our example as an extension of a commutative dynamical system via a unitary cocycle acting on a Hilbert bundle, and w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Positivity
سال: 2016
ISSN: 1385-1292,1572-9281
DOI: 10.1007/s11117-016-0422-4