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...

Poly(vinyl alcohol), PVA, is amenable to several structural modifications because of the presence of the hydroxyl moiety in the backbone. The chemical versatility of this polymer can be used for the obtainment of new wall-to-wall pH-responsive PVA chemical hydrogels and for the preparation of air-filled microspheres, for example, microbubbles. Here, we report on the characterization of the phys...

The host-guest complexation between an Alexa 488 labelled adamantane derivative and beta-cyclodextrin is studied by Fluorescence Correlation Spectroscopy (FCS). A 1:1 complex stoichiometry and a high association equilibrium constant of K = 5.2 x 10(4) M(-1) are obtained in aqueous solution at 25 degrees C and pH = 6. The necessary experimental conditions are discussed. FCS proves to be an excel...