On a functional representation of the lattice of projections on a Hilbert space
On extreme operators
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
On the geometry of and .
On the structure of positive maps between matrix algebras
The structure of the set of positive unital maps between M₂(ℂ) and Mₙ(ℂ) (n ≥ 3) is investigated. We proceed with the study of the "quantized" Choi matrix thus extending the methods of our previous paper [MM2]. In particular, we examine the quantized version of Størmer's extremality condition. Maps fulfilling this condition are characterized. To illustrate our approach, a careful analysis of Tang's maps is given.
One property of the weak convergence of operators iterations in von Neumann algebras.
Operators which respect norm intervals
Order theory and interpolation in operator algebras
In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. Here we continue to develop this positivity and its associated ordering, proving many foundational facts. We also give many applications, for example to noncommutative topology, noncommutative peak sets, lifting problems, peak interpolation, approximate identities, and to order relations between an operator...