1. CMB Online first
 Ino, Shoji

Perturbations of von Neumann subalgebras with finite index
In this paper, we study uniform perturbations of von Neumann
subalgebras of a von Neumann algebra.
Let $M$ and $N$ be von Neumann subalgebras of a von Neumann algebra
with finite probabilistic index in the sense of PimsnerPopa.
If $M$ and $N$ are sufficiently close,
then $M$ and $N$ are unitarily equivalent.
The implementing unitary can be chosen as being close to the
identity.
Keywords:von Neumann algebras, perturbations Categories:46L10, 46L37 

2. CMB 2011 (vol 56 pp. 136)
 Munteanu, RaduBogdan

On Constructing Ergodic Hyperfinite Equivalence Relations of NonProduct Type
Product type equivalence relations are hyperfinite measured
equivalence relations, which, up to orbit equivalence, are generated
by product type odometer actions. We give a concrete example of a
hyperfinite equivalence relation of nonproduct type, which is the
tail equivalence on a Bratteli diagram.
In order to show that the equivalence relation constructed is not of
product type we will use a criterion called property A. This
property, introduced by Krieger for nonsingular transformations, is
defined directly for hyperfinite equivalence relations in this paper.
Keywords:property A, hyperfinite equivalence relation, nonproduct type Categories:37A20, 37A35, 46L10 

3. CMB 2000 (vol 43 pp. 193)
 Magajna, Bojan

C$^*$Convexity and the Numerical Range
If $A$ is a prime C$^*$algebra, $a \in A$ and $\lambda$ is in the
numerical range $W(a)$ of $a$, then for each $\varepsilon > 0$ there
exists an element $h \in A$ such that $\norm{h} = 1$ and $\norm{h^*
(a\lambda)h} < \varepsilon$. If $\lambda$ is an extreme point of
$W(a)$, the same conclusion holds without the assumption that $A$ is
prime. Given any element $a$ in a von Neumann algebra (or in a
general C$^*$algebra) $A$, all normal elements in the weak* closure
(the norm closure, respectively) of the C$^*$convex hull of $a$ are
characterized.
Categories:47A12, 46L05, 46L10 
