Let H be an innite-dimensional Hilbert space over the field C, B(H) be the ∗-algebra of all linear bounded operators on H. An operator A ∈ B(H) is a commutator, if A = [S, T ] = ST - T S for some S, T ∈ B(H). Let X, Y ∈ ...

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):.

We establish similarity between some tripotents and idempotents on a Hilbert space $H$ and obtain new results on differences and commutators of idempotents $P$ and $Q$. In the unital case, the difference $P - Q$ is associated ...

© 2018, Pleiades Publishing, Ltd. Suppose that M is a von Neumann algebra of operators on a Hilbert space H and τ is a faithful normal semifinite trace on M. Let E, F and G be ideal spaces on (M, τ). We find when a ...

In this paper, we present new properties of the space L1(M, τ) of integrable (with respect to the trace τ) operators affiliated to a semifinite von Neumann algebra M. For self-adjoint τ-measurable operators A and B, we ...

Для грубых операторов типа Хаусдорфа, определенных на p-адическом линейном про- странстве Q n p , и их коммутаторов с символом из пространства Липшица мы приво- дим достаточные условия их ограниченности из одного пространства ...