Absolute continuity for operator valued completely positive maps on C∗-algebras

On positive operator-valued continuous maps

In the paper the geometric properties of the positive cone and positive part of the unit ball of the space of operator-valued continuous space are discussed. In particular we show that ext-ray C+(K,L(H)) = {R+1{k0}x⊗ x : x ∈ S(H), k0 is an isolated point of K} ext B+(C(K,L(H))) = s-ext B+(C(K,L(H))) = {f ∈ C(K,L(H) : f(K) ⊂ ext B+(L(H))}. Moreover we describe exposed, strongly exposed and denti...

Covariant Completely Positive Linear Maps between Locally C-algebras

We prove a covariant version of the KSGNS (Kasparov, Stinespring, Gel’fand,Naimark,Segal) construction for completely positive linear maps between locally C-algebras. As an application of this construction, we show that a covariant completely positive linear map ρ from a locally C-algebra A to another locally C -algebra B with respect to a locally C-dynamical system (G,A,α) extends to a complet...

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

Irreducible Positive Linear Maps on Operator Algebras

Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible...