Consider a unital $C^*$-algebra $\mathcal{A}$. Let $n\geq 2$ and let $P_1, \ldots , P_n$ be projections in $\mathcal{A}$ such that $P_1 + \ldots +P_n=I$. We costruct $\mathcal{P}_n\colon \mathcal{A}\to \mathcal{A}$ ...
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 ...
We generalized the C. R. Putnam theorem (1951), see also Problem 188 in the book (P. R. Halmos, A Hilbert space problem book. D. van Nostrand company, inc., London, 1967):.
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 ...