© 2015, Pleiades Publishing, Ltd. Let M be a von Neumann algebra of operators in a Hilbert space H, let τ be an exact normal semifinite trace on M, and let L1(M, τ) be the Banach space of τ-integrable operators. The following ...

© 2014, Pleiades Publishing, Ltd. Let τ be a faithful normal semifinite trace on the von Neumann algebra M, 1 ≥ q > 0. The following generalizations of problems 163 and 139 from the book [1] to τ-measurable operators are ...

© 2014, Pleiades Publishing, Ltd. Let A be a unital algebra over complex field ℂ, I be the unit of A. An element A ∈ A is called tripotent if A3 = A. Let Atri = {A ∈ A: A3 = A}. We show that A ∈ Atri if and only if I ± A ...