Duality and operator algebras: automatic weak* continuity and applications

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

Duality and Operator Algebras

We investigate some subtle and interesting phenomena in the du-ality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are always weak *-continuous on dual operator spaces. For example , if X is a subspace of a C *-algebra A, and if a ∈ A satisfies aX ⊂ X and a * X ⊂ X, and if X i...

automatic continuity of homomorphisms between banach algebras and frechet algebras

Automatic Continuity of Higher Derivations on JB*-Algebras

Crossed Products of Operator Algebras: Applications of Takai Duality

Let (G,Σ) be an ordered abelian group with Haar measure μ, let (A,G, α) be a dynamical system and let A oα Σ be the associated semicrossed product. Using Takai duality we establish a stable isomorphism Aoα Σ ∼s ( A⊗K(G,Σ, μ) ) oα⊗Ad ρ G, where K(G,Σ, μ) denotes the compact operators in the CSL algebra AlgL(G,Σ, μ) and ρ denotes the right regular representation of G. We also show that there exis...