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 ...
We obtain an estimate of the norm of the Lagrange interpolation operator in a multidimensional Sobolev space. It is shown that, under a suitable choice of the sequence of multi-indices, interpolation polynomials converge ...
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 ...
Let H be a complex Hilbert space with conjugation operator J. We study J-real operators and we have covered J-regular subspaces. We prove that for given bounded idempotent p there exists a conjugation operator J0 such that ...
We consider a von Neumann algebra $M$ acting on a
Hilbert space $H$. For a positive operator $X$ in $M$ we define the
operator ``intervals'' $I_X=\{Y=Y^*\in M: \; -X \leq Y \leq X \}$ and
$L_X=\{Y \in M: \; |Y| \leq X ...
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 ...