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 ...
Let B(H) Id be the set of all bounded idempotents on a complex Hilbert space H and let J be a conjugation operator on H. Fix p ∈ B(H) Id. At the paper we describe of J-projections. We prove that for a given p there exists ...
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 ...
We study invertibility of some sums of linear bounded operators on Hilbert space (Theorem 1). A criterion on invertibility of sums of projections is found. Some equivalent conditions on invertibility of difference of two ...
We describe the class of translation invariant measures on the algebra B(H) of bounded
linear operators on a Hilbert space H and some of its subalgebras. In order to achieve this we apply
two steps. First we show that a ...