Abstract: It is proved that the inequality (Formula presented.) characterizes tracial functionals among all positive normal functionals ϕ on a von Neumann algebra A. This strengthens the L. T. Gardner’s characterization ...
We obtain new necessary and sufficient commutation conditions for projections in terms of operator inequalities. These inequalities are applied for trace characterization on von Neumann algebras for the class of all positive ...
We find new necessary and sufficient conditions for the commutativity of projections in terms of operator inequalities. We apply these inequalities to characterize a trace on von Neumann algebras in the class of all positive ...
Consider a von Neumann algebra M with a faithful normal semifinite trace τ. We prove that each order bounded sequence of τ-compact operators includes a subsequence whose arithmetic averages converge in τ. We also prove a ...
We obtain a description of all pairs of Hermitian operators X and Y, which satisfy the condition -Y ≤ X ≤ Y. We give the examples of such operator pairs. Each of the presented examples leads us to the new weak majorization ...
Abstract: We consider a tracial state ϕ on a von Neumann algebra A and assume that projections P, Q of A are independent if ϕ(PQ) = ϕ(P)ϕ(Q). First we present the general criterion of a projection pair independence. We ...