Perturbations of centre-fixing dynamical systems.
In this paper, we introduce Pexiderized generalized operators on certain special spaces introduced by Bielecki-Czerwik and investigate their norms.
This is a survey article about a theory of a Poisson boundary associated with a discrete quantum group. The main problem of the theory, that is, the identification problem is explained and solved for some examples.
A new proof is obtained to the following fact: a Rickart C*-algebra satisfies polar decomposition. Equivalently, matrix algebras over a Rickart C*-algebra are also Rickart C*-algebras.
We present recent results on positive energy representations of quantum spin models.
A characterization of the structure of positive maps is presented. This sheds some more light on the old open problem studied both in Quantum Information and Operator Algebras. Our arguments are based on the concept of exposed points, links between tensor products and mapping spaces and convex analysis.
For C*-algebras A and B and a Hilbert space H, a class of bilinear maps Φ: A× B → L(H), analogous to completely positive linear maps, is studied. A Stinespring type representation theorem is proved, and in case A and B are commutative, the class is shown to coincide with that of positive bilinear maps. As an application, the extendibility of a positive operator bimeasure to a positive operator measure is shown to be equivalent to various conditions involving positive scalar bimeasures, pairs of...