Hilbertian operators and reflexive tensor products

Spectra of Tensor Products of Operators

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...

^-convolution Operators and Tensor Products of Banach Spaces

intimately connected with duality theory (the notation is that of [1]). In both cases the middle algebra is the closure of L(G) in the dual of the first algebra and also the predual of the third algebra (at least when G is amenable in the second case). Furthermore, the third algebra is closely connected with the multiplier algebra of the first algebra. For abelian groups, compact or discrete, V...

Hilbert-Schmidt operators and tensor products of Hilbert spaces

Let V ⊗HS W be the completion of V ⊗alg W in the norm defined by this inner product. V ⊗HS W is a Hilbert space; however, as Garrett shows it is not a categorical tensor product, and in fact if V and W are Hilbert spaces there is no Hilbert space that is their categorical tensor product. (We use the subscript HS because soon we will show that V ⊗HS W is isomorphic as a Hilbert space to the Hilb...

Universality and chaos for tensor products of operators

We give sufficient conditions for the universality of tensor products fTnf #Rn : nANg of sequences of operators defined on Fréchet spaces. In particular we study when the tensor product Tf #R of two operators is chaotic in the sense of Devaney. Applications are given for natural operators on function spaces of several variables, in Infinite Holomorphy, and for multiplication operators on the al...