On automorphisms of type Arveson systems (probabilistic approach).
On AW*-subalgrebras of type I AW*-algebras.
On Banach algebras satisfying a spectral maximum principle
On basic concepts of non-commutative topology
On bounded module maps between Hilbert modules over locally -algebras.
On -algebras associated to certain endomorphisms of discrete groups.
On C*-algebra extensions relative to a factor of type II...
On C*-algebras having linear, polynomial and subexponential growth.
On Cartan Homotopy Formulas in Cyclic Homology.
On certain properties of the relative entropy of states of operator algebras.
On Classes of Projections in a von Neumann Algebra.
On commutative algebras of unbounded operators
On commuting C*-algebras of operators.
On completely bounded bimodule maps over W*-algebras
It is proved that for a von Neumann algebra A ⊆ B(ℋ ) the subspace of normal maps is dense in the space of all completely bounded A-bimodule homomorphisms of B(ℋ ) in the point norm topology if and only if the same holds for the corresponding unit balls, which is the case if and only if A is atomic with no central summands of type . Then a duality result for normal operator modules is presented and applied to the following problem. Given an operator space X and a von Neumann algebra A, is the map...
On derivations and crossed homomorphisms
We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer true, in general,...
On Ergodic Flows and the Isomorphism of Factors.
On ergodic properties of convolution operators associated with compact quantum groups
Recent results of M. Junge and Q. Xu on the ergodic properties of the averages of kernels in noncommutative -spaces are applied to the analysis of almost uniform convergence of operators induced by convolutions on compact quantum groups.
On extremal positive maps acting between type I factors
The paper is devoted to the problem of classification of extremal positive linear maps acting between 𝔅(𝒦) and 𝔅(ℋ) where 𝒦 and ℋ are Hilbert spaces. It is shown that every positive map with the property that rank ϕ(P) ≤ 1 for any one-dimensional projection P is a rank 1 preserver. This allows us to characterize all decomposable extremal maps as those which satisfy the above condition. Further, we prove that every extremal positive map which is 2-positive turns out to be automatically completely...
On full Hilbert -modules.
On generalized inverses in C*-algebras
We investigate when a C*-algebra element generates a closed ideal, and discuss Moore-Penrose and commuting generalized inverses.