We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups from several angles. give a short, elementary proof that finitely generated nilpotent are HS-stable. investigate the permanence HS-stability under central quotients by showing is preserved finite quotients, but not in general. characterization for semidirect products G⋊γZ with G abelian. use it to construct first ex...

We characterize left and right amenable semigroups of polynomials one complex variable with respect to the composition operation. also prove a number results about arbitrary rational functions. In particular, we show that under quite general conditions semigroup functions is if only it subsemigroup centralizer some function.

Abstract What is the probability that a random UHF algebra of infinite type? simple AI has at most k extremal traces? expected value radius comparison Villadsen-type AH algebra? such an $\mathcal{Z}$ -stable? Cuntz–Krieger purely and simple, what can be said about distribution its K -theory? By constructing $\mathrm{C}^*$ -algebras associated with suitable (walks on) graphs, we provide context ...

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

In the theory of operator algebras, classification of group actions on approximately finite dimensional (AFD) factors has been done since Connes’s work [2]. In subfactor theory, various results on classification of group actions have been obtained. The most powerful results have been obtained by Popa in [16], who classified the strongly outer actions of discrete amenable groups on strongly amen...

We prove a classification result for properly outer actions σ of discrete amenable groups G on strongly amenable subfactors of type II, N ⊂ M , a class of subfactors that were shown to be completely classified by their standard invariant GN,M , in ([Po7]). The result shows that the action σ is completely classified in terms of the action it induces on GN,M . As a an application of this, we obta...

in the present paper, the concepts of module (uniform) approximate amenability and contractibility of banach algebras that are modules over another banach algebra, are introduced. the general theory is developed and some hereditary properties are given. in analogy with the banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

The ionic liquid, N,N,N,N-tetramethylguanidiniumtriflate (TMGTf) was found to be an efficient catalyst solvent for Henry reaction between nitromethane and isatin derivatives to provide 3-hydroxy-3-(nitromethyl)indolin-2-one under mild conditions. The ionic liquid amenable to successive recycling without appreciable decrease in activity. Synthesized compounds have been screened for their anti-di...