In the paper a new approach is proposed to construction of operator algebras generated by multi-valued mappings on a countable set. We present initial results, discuss the connection with known structures, outline further ...

We prove that a real function is operator monotone (operator convex) if the corresponding monotonicity (convexity) inequalities are valid for some normal state on the algebra of all bounded operators in an infinite-dimensional ...

We study inequalities of the form, where τ is a trace on a von Neumann algebra or a C*-algebra, A and B are self-adjoint elements of the algebra in question, f and w are real-valued functions, and the "weight" function w ...