Schedule-at-a-Glance

33 PRIMA 2013 Abstractssense. Our approach does not involve invariant means forG.p-variations of Fourier algebrasNico SpronkUniversity of Waterloo, Canadanspronk@uwaterloo.caLet G be a compact group and A(G) its Fourier algebra.About a half decade ago, an invesitgation of B. Forrest,E. Samei and the speaker brought up a curious Banachalgebra A ∆ (G) which plays a role relative to operatoramenability problems for A(G), in the same manner as acertain algebra A γ(G) of B. Johnson plays to amenabilityproblems. The algebra A γ(G) may be understoodas a type of “Beurling-Fourier algebra" on G, in a mannerwhich has been recently invesigated by H.H. Lee, E.Samei, J. Ludwig, L. Turowska and the speaker, in variousarticles.I will present a context in which we may understandA ∆ (G) as the case p = 2 in a class of Banach algebrasA p (G) (1 ≤ p ≤ ∞). Here A 1 (G) = A(G), but the rest ofthe algebras may be understood via interpolation. Thesealgebras do not exhibit the same functorial properties asFourier algebras, and hence allow us to exhibit some unusualBanach algebras on tori.This talk represents joint work with H.H. Lee and E.Samei.Zero products and norm preserving orthogonallyadditive homogeneous polynomials onC*-algebrasNgai-Ching WongNational Sun Yat-sen University, Taiwanwong@math.nsysu.edu.twLet P : A → B be a bounded orthogonally additiveand zero product preserving n-homogeneous polynomialbetween C*-algebras. We show that, in the commutativecase that A = C 0 (X) and B = C 0 (Y ), there exista bounded continuous function h in C(Y ) and a mapϕ : Y → X such that P f = h · (f ◦ ϕ) n . In the generalcase, we show that there is a central invertible multiplierh of B and a surjective Jordan homomorphism J : A → Bsuch that P a = hJ(a) n , provided that P (A) ⊇ B + . SimilarBanach-Stone type theorems also hold for orthogonallyadditive n-homogeneous polynomials which are n-isometries. Using these results, we provide the full structureof orthogonally additive and orthogonally multiplicativeholomorphic functions on commutative C*-algebras.This is a joint work with Qingying Bu (Univ. of Mississippi)and Ming-Hsiu Hsu (Nat’l Sun Yat-sen Univ.)Recent development of analysis on noncommutativetoriQuanhua XuWuhan University, China and University of Franche-Comté, FranceNoncommutative tori are fundamental examples in operatoralgebras and noncommutative geometry. This talkwill present a survey on the recent development of analysison noncommutative tori. The results presented willinclude those on harmonic analysis and Sobolev embeddinginequalities on quantum tori. This talk is based onjoint works with Zeqian Chen, Xiao Xiong and Zhi Yin.Amenability properties of weighted group algebrasYong ZhangUniversity of Manitoba, Canadazhangy@cc.umanitoba.caLet G be a locally compact group and ω a continuousweight on G. It is well-known that the weightedgroup algebra L 1 (G, ω) is amenable as a Banach algebraif and only if G is an amenable group and the functionΩ(t) = ω(t)ω(t −1 ) is bounded on G. We show that, foran abelian locally compact group G, L 1 (G, ω) is weaklyamenable if and only if there is no nontrivial continuousgroup homomorphism φ: G → (C, +) such that|φ(t)|supt∈G Ω(t) < ∞.In other words, Ω(t) shall grow slower then any φ in orderL 1 (G, ω) to be weakly amenable.We will also consider the weak amenability of L 1 (G, ω)and its center ZL 1 (G, ω) for non-commutative locallycompact groups G, discussing some special cases. In general,how to characterize the weak amenability of a noncommutativeL 1 (G, ω) and how to characterize the weakamenability of its center algebra are still open problems.Special Session 17OptimizationRegularized interior proximal alternating directionsmethodFelipe AlvarezUniversidad de Chile, Chilefalvarez@dim.uchile.clWe consider convex constrained optimization problemswith a special separable structure. We propose a class ofalternating directions methods (ADM) where their subproblemsare regularized with a general interior proximalmetric which covers the double regularization proposed bySilva and Eckstein. Under standard assumptions, globalconvergence of the primal-dual sequences produced by thealgorithm is established.Linear conic programming and interior-pointalgorithmsYanqin BaiShanghai University, Chinayqbai@shu.edu.cnLinear conic programming extends the popularly used linearprogramming models from linearity to non-linearityas well as from convexity to non-convexity in polynomialtimecomputations. Linear conic programming problemsare linear programming models with the additional constraintof products of nonlinear cones which include twoclasses of important cones. One class is symmetric conewhich leads to symmetric cone optimization problemssuch as linear, semideąěnite and second-order cone programmingproblems in which the cone constraints are selfdualand homogeneous. These symmetric conic programmingcan be solved eąÀciently using polynomial-timeinterior-point methods. Another class is nonsymmetriccone optimization problems such as copositive cone programmingproblems and the cone programming of nonnegativequadratic function over a set. For these conicprogramming the cone constraints are not self-dual andin particular requires special purpose algorithm. The proposeof this talk is to introduce a very rich formulation oflinear conic programming and present the general model,the conjugate duality theory, path-following interior pointapproaches and illustrative applications of linear conicprogramming.