Completely bounded maps on $C\sp{\ast} $-algebras and invariant operator ranges

On topological transitive maps on operator algebras

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

Multiplicative bijective maps on standard operator algebras

Completely Bounded Maps into Certain Hilbertian Operator Spaces

We prove a factorization of completely bounded maps from a C *-algebra A (or an exact operator space E ⊂ A) to ℓ 2 equipped with the operator space structure of (C, R) θ (0 < θ < 1) obtained by complex interpolation between the column and row Hilbert spaces. More precisely, if F denotes ℓ 2 equipped with the operator space structure of (C, R) θ , then u : A → F is completely bounded iff there a...

Representations of Multiplier Algebras in Spaces of Completely Bounded Maps

If G is a locally compact group, then the measure algebra M(G) and the completely bounded multipliers of the Fourier algebra McbA(G) can be seen to be dual objects to one another in a sense which generalises Pontryagin duality for abelian groups. We explore this duality in terms of representations of these algebras in spaces of completely bounded maps. This article is intended to give a tour of...

Representations of Group Algebras in Spaces of Completely Bounded Maps

Let G be a locally compact group, π : G → U(H) be a strongly continuous unitary representation, and CB(B(H)) the space of normal completely bounded maps on B(H). We study the range of the map Γπ : M(G)→ CB(B(H)), Γπ(μ) = Z G π(s)⊗ π(s)dμ(s) where we identify CB(B(H)) with the extended Haagerup tensor product B(H)⊗ B(H). We use the fact that the C*-algebra generated by integrating π to L(G) is u...