Schedule-at-a-Glance

32 PRIMA 2013 Abstractsgroup G, where T (L 2 (G)) is the space of trace class operatorson L 2 (G) with the convolution induced by theright fundamental unitary of G. We obtain a natural isomorphismbetween the completely bounded right multiplieralgebras of L 1 (G) and T (L 2 (G)), and characterizethe regularity of the quantum group G in terms of theconvolution on T (L 2 (G)). We show that T (L 2 (G)) isstrongly Arens irregular in the sense of Dales and Lauif and only if G is finite. Some commutation relationsof completely bounded multipliers of L 1 (G) will also bediscussed. This is joint work with Matthias Neufang andZhong-Jin Ruan.Complex geometry and similarity of Cowen-Douglas operatorsChunlan JiangHebei Normal University, Chinacljiang@hebtu.edu.cnIn this talk, we discuss the similarity invariant of the geometryoperator induced by the holomorphic bundle. Wegive a complete similarity invariant of this kind of geometryoperator by using K-group and curvature.Minimum phase operators and the Polya-Schur problemMichael P. LamoureuxUniversity of Calgary, Canadamikel@ucalgary.caWe set a mathematical framework for understanding minimumphase preserving physical processes and obtain thefollowing. The natural analytic setting for these timelimitedsignals is Hilbert-Hardy space. The minimumphase (or impulsive) signals correspond to the outer functionsin Hardy space. The minimum phase preservingprocesses correspond to linear operators which preservethe set of shifted outer functions.Our main result shows these linear operators on Hardyspace are completely characterized as a combination ofa multiplication and a composition operator involvingholomorphic functions of a specific form. The proof ofthis result makes essential use of Hadamard’s Theoremand the Weierstrass product representation. Remarkably,this result also extends to provide constructive solutionsto the Polya-Schur problem of finding linear operatorsthat preserve the zero-sets of families of complex polynomials.Returning to the physical problem, these processesthus consist of a stationary filtering combined witha frequency-dependent Q-attenuation.Joint with Peter. C. Gibson and Gary F. MargraveKishimoto’s conjugacy theorems in simple C ∗ -algebras of tracial rank oneHuaxin LinUniversity of Oregon, USAhlin@uoregon.eduLet A be a unital separable simple amenable C*-algebrawith finite tracial rank which satisfies the UCT. Supposeα and β are two automorphisms with the Rokhlin property.We show that α and β are strongly co-cycle conjugateand uniformly approximately conjugate, i.e., thereexists a sequence of unitaries {u n} ⊂ A and a sequence ofstrong asymptotically inner automorphisms σ n such thatα = Ad u n ◦ σ n ◦ β ◦ βn −1 and lim ‖un − 1‖ = 0,n→∞provided that they induce the same K-theoretical data.We also show that converse also holds. We also give aK-description as exactly when α and β are co-cycle conjugate.We also show that given a K-theoretical data,there is an automorphism α with the Rokhlin propertywhich has that given K-theoretical data.Spectral gap actions and invariant statesChi-Keung NgNankai University, Chinackng@nankai.edu.cnWe define spectral gap actions of discrete groups on vonNeumann algebras and study their relations with invariantstates. We will show that a finitely generated ICCgroup Γ is inner amenable if and only if there exist morethan one inner invariant states on the group von Neumannalgebra L(Γ). Moreover, a countable discrete groupΓ has property (T ) if and only if for any action α of Γ ona von Neumann algebra N, every α-invariant state on Nis a weak- ∗ -limit of a net of normal α-invariant states.Quantum correlations and Tsirelson’s problemNarutaka OzawaKyoto University, Japannarutaka@kurims.kyoto-u.ac.jpThe EPR paradox tells us quantum theory is incompatiblewith classic realistic theory. Indeed, Bell has shownthat quantum correlations of independent bipartite systemshave more possibility than the classical correlations.To study what the possibilities are, Tsirelson has introducedthe set of quantum correlation matrices, but dependingon the interpretation of independence, there aretwo plausible definitions of it. Tsirelson’s problem askswhether these definitions are equivalent. It turned outthat this problem in quantum information theory is infact equivalent to Connes’s embedding conjecture, one ofthe most important open problems in theory of operatoralgebras. I will talk some recent progress on Tsirelson’sproblem.Ergodic theory over locally compact quantumgroupsVolker RundeUniversity of Alberta, Canadavrunde@ualberta.caWe develop the elements of an ergodic theory over locallycompact quantum (semi)groups and extend resultsby Zsidó et al.. This is joint work with Ami Viselter.Extending derivations to dual Banach algebrasEbrahim SameiUniversity of Saskatchewan, Canadasamei@math.usask.caIf D : A → X is a derivation from a Banach algebra toa contractive, Banach A-bimodule, then one can equipX ∗∗ with an A ∗∗ -bimodule structure, such that the secondtranspose D ∗∗ : A ∗∗ → X ∗∗ is again a derivation.I present an analogous extension result, where A ∗∗ is replacedby the enveloping dual Banach algebra F(A) (as introducedby V. Runde), and X ∗∗ by an appropriate kindof universal, enveloping, normal dual bimodule of X. Ourapproach is motivated by earlier results of F. Gourdeau.I apply these constructions to obtain some new characterizationsof Connes-amenability of F(A). In particular, weshow that F(A) is Connes-amenablity if and only if A admitsa so-called WAP-virtual diagonal. Also, in the casewhere A = L 1 (G), we show by modifying arguments ofRunde that existence of a WAP-virtual diagonal is equivalentto the existence of a virtual diagonal in the usual