Pairing and Quantum Double of Finite Hopf C^＊-Algebras

This paper defines a pairing of two finite Hopf C^＊-algebras A and B, and investigates the interactions between them. If the pairing is non-degenerate, then the quantum double construction is given. This construction yields a new finite Hopf C^＊-algebra D（A, B）. The canonical embedding maps of A and B into the double are both isometric.     

Synthesis and mesomorphic properties of new compounds exhibiting TGBA and TGBC liquid crystalline phases

We synthesised a series of rod-like mesogens with a (S)-2-methylbutyl-(S)-lactate unit in the chiral chain that exhibited extremely wide temperature ranges in the TGBA and TGBC* phases. TGB phases were identified, based on typical textures in confined samples and in free-standing films, by Grandjean-Cano texture and by NMR studies on a deuterium-labelled isotopomer. A sufficiently high electric or magnetic field transformed the TGBA and TGBC* phases into their respective SmA and SmC* phases, the TGB structures being restored within some 20-30 minutes. Therefore values of the spontaneous polarisation and spontaneous tilt angle, when measured under a sufficiently high field, gave evidence of the properties of the SmC* phase. Temperature dependencies of relaxation frequency, dielectric strength, selective reflection and layer spacing showed anomalies at a certain temperature within the TGBC* phase range. Also, changes in textures, as well as in ²H-NMR spectra, occurred at this same temperature. These results suggest the existence of two TGBC* phases.     

AN EXISTENCE THEOREM FOR MAXIMAL ELEMENTS AND ITS APPLICATIONS

An existence theorem of maximal elements for an L＊-majorized correspondence defined on a non-paracompact H-space is established. As applications of the result, an equilibrium existence theorem for a non-paracompact generalized game in H-spaces with infinitely many players and with L＊-majorized correspondences is given.     

Uniqueness of the trace and simplicity

It is proved that for certain large classes of unital C*-algebras, the existence of a unique, faithful tracial state implies simplicity. An example is given to show that this implication does not hold for all unital C*-algebras.

     

空间的-特殊点可数族使其为D-空间

本文给出了空间为D-空间的-充分条件,主要结论如下:如果空间X有一点可数族F,满足对X的任-子集A (C) X,若A在X中不闭,都存在某点x ∈-A\A,使得对X的任一开集U,若X∈U,都存在某个F∈F,使得X ∈F(C) U且F ∩ A≠ (θ),则X是D-空间.由此结论,我们得到-序列空间若有点可数cs*-网络,则X是D-空间.     

Deformations of the central extension of the Poisson superalgebra

The Poisson superalgebra realized on smooth Grassmann-valued functions with compact support has a central extension at some values of the superdimension. We find formal deformations of these central extensions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 250–269, August, 2008.     

Real Banach ✶ Algebras

In this paper, we study real Banach ✶ algebras systematically. We present the right form of Pták's inequality [1,4] in the real case, and generalize the results of Vukman in [3] to the general case (algebras with or without an identity). Moreover, this paper is a real analogue of Pták's work [1] in the complex case. Received February 22, 2000, Accepted March 14, 2000     

置换空间中的最佳逼近存在性与唯一性定理

得到了置换空间PXXn中的最佳逼近存在性与唯一性定理.     

迹稳定秩1的C~*-代数的稳定有限性与弱迹稳定秩1

主要给出了迹稳定秩1的C~*-代数的稳定有限性,证明了如果A是有单位元迹稳定秩1的C~*-代数,则A是稳定有限的,引入了弱迹稳定秩1的定义,并且证明了如果有单位元的C~*-代数A是迹稳定秩1的,则A是弱迹稳定秩1的．对于单的具有SP性质的有单位元的C~*-代数A,如果A是弱迹稳定秩1的,则A是迹稳定秩1的．同时给出了迹稳定秩1的C~*-代数的一个等价条件,证明了一个有单位元的可分的C~*-代数A是迹稳定秩1的,等价于A=(t_4)limn→∞(A_n,p_n),其中tsr(A_n)=1．