Infinite tensor products of operators

Spectra of Tensor Products of Operators

Tensor Products of Theories, Application to Infinite Loop Spaces*

In [4] Lawvere formalized the concept of an algebraic theory defined by operations and laws without existential quantifiers. Examples are the theories of monoids, groups, loops, rings, modules etc., whose axioms can be put into the required form; although not the theory of fields. The advantage of this approach lies in the unified treatment of a variety of universal constructions, especially th...

Convergence of Generic Infinite Products of Affine Operators

Our goal in this paper is to study the asymptotic behavior of random infinite products of generic sequences of affine uniformly continuous operators on bounded closed convex subsets of a Banach space. Infinite products of operators find application in many areas of mathematics (cf. [1, 2, 3, 8, 9, 10] and the references therein). More precisely, we show that in appropriate spaces of sequences o...

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...