Operator synthesis and tensor products

On Tensor Products of Operator Modules

The injective tensor product of normal representable bimodules over von Neumann algebras is shown to be normal. The usual Banach module projective tensor product of central representable bimodules over an Abelian C∗-algebra is shown to be representable. A normal version of the projective tensor product is introduced for central normal bimodules.

Diagonals in Tensor Products of Operator Algebras

In this paper we give a short, direct proof, using only properties of the Haagerup tensor product, that if an operator algebra A possesses a diagonal in the Haagerup tensor product of A with itself, then A must be isomorphic to a finite dimensional C∗-algebra. Consequently, for operator algebras, the first Hochschild cohomology group, H(A, X) = 0 for every bounded, Banach A-bimodule X , if and ...

Hilbert Modules and Tensor Products of Operator Spaces

The classical identification of the predual of B(H) (the algebra of all bounded operators on a Hilbert space H) with the projective operator space tensor product H⊗̂H is extended to the context of Hilbert modules over commutative von Neumann algebras. Each bounded module homomorphism b between Hilbert modules over a general C∗-algebra is shown to be completely bounded with ‖b‖cb = ‖b‖. The so ca...

bivariations and tensor products

the ordinary tensor product of modules is defined using bilinear maps (bimorphisms), that are linear in eachcomponent. keeping this in mind, linton and banaschewski with nelson defined and studied the tensor product in an equational category and in a general (concrete) category k, respectively, using bimorphisms, that is, defined via the hom-functor on k. also, the so-called sesquilinear, or on...

The Haagerup Invariant for Tensor Products of Operator Spaces