Derivations in Commutative Regular Algebras

Mathematical Notes -     

Interpolation of positive operators

We study problems of interpolation of positive linear operators in couples of ordered Banach spaces. From this viewpoint, we study couples of noncommutative spaces L ₁, L _∞ associated with weights and traces on von Neumann algebras.     

The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.     

Isometries of symmetric operator spaces associated with AFD factors of typeII and symmetric vector-valued spaces

If is a surjective isometry of the separable symmetric operator spaceE(M, ) associated with the approximately finite-dimensional semifinite factorM and if · _E(M,) is not proportional to · _{L 2}, then there exist a unitary operatorUM and a Jordan automorphismJ ofM such that(x)=UJ(x) for allxME(M, ). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, )).Research supported by the Australian Research Council     

Characterizations of Kadec-Klee properties in symmetric spaces of measurable functions

We present several characterizations of Kadec-Klee properties in symmetric function spaces on the half-line, based on the -functional of J. Peetre. In addition to the usual Kadec-Klee property, we study those symmetric spaces for which sequential convergence in measure (respectively, local convergence in measure) on the unit sphere coincides with norm convergence.

     

Kinetic and mechanistic study of the quasiliving cationic polymerization of styrene with the 2-phenyl-2-propanol/AlCl3 · OBu2 initiating system

The cationic polymerization of styrene with the 2-phenyl-2-propanol (CumOH)/AlCl₃ · OBu₂ initiating system at various dibutyl ether concentrations in a mixture of 1,2-dichloroethane and n-hexane (55:45 v/v) at −15 °C was investigated. The experimental results showed that an increase in dibutyl ether concentration leads to a noticeable decrease in the polymerization rate as well as to the more controlled polymerization in terms of molecular weight (M_n) and molecular weight distribution (MWD) evolutions. The kinetic investigation revealed that the polymerization proceeds in two stages. The first stage is characterized by high polymerization rate and slow initiation relative to propagation. During this stage molecular weight decreases or does not change and MWD increases with conversion. In the second stage considerably slower quasiliving polymerization of styrene occurs. The quasiliving nature of the styrene polymerization by the CumOH/AlCl₃ · OBu₂ system is proved and mechanistic scheme of the polymerization is proposed.     

Koplienko Spectral Shift Function on the Unit Circle

The note shows that, for every pair of contractions, a trace formula of Koplienko holds with a summable spectral shift function, see Theorem 1 below. This answers a question by F. Gesztesy, A. Pushnitski, B. Simon (see Zh Mat Fiz Anal Geom 4(1):63–107, 202, 2008, Open Question 11.2).     

Banach limits: Invariance and functional characteristics

Banach limits invariant with respect to the Cesàro transform are studied. New functional characteristics of Banach limits are introduced and studied.     

Morphology of integral (structural) polymer foams

The survey deals with the fundamental morphological parameters of integral (structural) polymer foams, which have a specific structure: a cellular core that gradually turns into a solid skin. Attempts are made to evaluate the effect and the contribution of the main parameters (the core, the skin, and the intermediate zone) on the strength properties of these foams. Further problems in the morphology of integral foams are discussed.