Tensor products of measurable operators

Spectra of Tensor Products of Operators

Submajorization inequalities associated with $tau$-measurable operators

The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..

Quasi *-algebras of Measurable Operators

Non-commutative L-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algeb...

Resolvents of operators on tensor products of Euclidean spaces

We consider the operator T = m k=1 A 1k ⊗ A 2k (1 ≤ m < ∞), where A lk are n l × n l matrices (k = 1,. .. , m; l = 1, 2), ⊗ means the tensor product. Norm estimates for the resolvent of that operator are derived. By these estimates, we obtain bounds for a solution X of the equation m k=1 A 1k X A 2k = C and explore perturbations of that equation. The norm estimates for the resolvent of T enable...

Tensor Products of Holomorphic Representations and Bilinear Differential Operators

Let be weighted Bergman space on a bounded symmetric domain . It has analytic continuation in the weight and for in the so-called Wallach set still forms unitary irreducible (projective) representations of . We give the irreducible decomposition of the tensor product of the representation for any two unitary weights and we find the highest weight vectors of the irreducible components. We find a...