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21.
This is a collection of open problems which touch on Neil Hindman's mathematics and were collected in conjunction with the Conference on Ramsey Theory and Topological Algebra in his honor. 相似文献
22.
We continue our work [E. Kaniuth, A.T. Lau, J. Pym, On φ-amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc. 144 (2008) 85-96] in the study of amenability of a Banach algebra A defined with respect to a character φ of A. Various necessary and sufficient conditions of a global and a pointwise nature are found for a Banach algebra to possess a φ-mean of norm 1. We also completely determine the size of the set of φ-means for a separable weakly sequentially complete Banach algebra A with no φ-mean in A itself. A number of illustrative examples are discussed. 相似文献
23.
For a locally compact group G and 1<p<∞ let Ap(G) be the Figà-Talamanca–Herz algebras, which include in particular the Fourier algebra of G , A(G) (p=2). It is shown that for any amenable group H , a proper affine map α:Y⊂H→G induces a p -completely contractive algebra homomorphism ?α:Ap(G)→Ap(H) by setting ?α(u)=u°α on Y and ?α(u)=0 off of Y. Moreover, we show that if both G and H are amenable then any p -completely contractive algebra homomorphism ?:Ap(G)→Ap(H) is of this form. These results are the analogs in the context of the Figà-Talamanca–Herz algebras of the ones in the Fourier algebra setting (p=2) initiated by the author and continued with N. Spronk, which in turn generalize results of P.J. Cohen and B. Host from abelian group algebra setting. 相似文献
24.
We will study some permanence properties of C*-unique groups in details. In particular, normal subgroups and extensions will be considered. Among other interesting results, we prove that every second countable amenable group with an injective finite-dimensional representation (not necessarily unitary) is a retract of a C*-unique group. Moreover, any amenable discrete group is a retract of a discrete C*-unique group. 相似文献
25.
Gá bor Elek Gá bor Tardos 《Proceedings of the American Mathematical Society》2000,128(8):2479-2485
We introduce the notion of rough transitivity and prove that there exist no non-constant harmonic Dirichlet functions on amenable roughly transitive graphs.
26.
The local properties of entropy for a countable discrete amenable group action are studied. For such an action, a local variational principle for a given finite open cover is established, from which the variational relation between the topological and measure-theoretic entropy tuples is deduced. While doing this it is shown that two kinds of measure-theoretic entropy for finite Borel covers coincide. Moreover, two special classes of such an action: systems with uniformly positive entropy and completely positive entropy are investigated. 相似文献
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28.
Let M be a semisimple left module of finite length over a ring R and let G be an amenable group. We show that an R-linear cellular automaton τ:MG → MG is surjective if and only if it is pre-injective. 相似文献
29.
We introduce iterative algorithms for finding a common element of the set of solutions of a system of equilibrium problems and of the set of fixed points of a finite family and a left amenable semigroup of nonexpansive mappings in a Hilbert space. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. Our results extend, for example, the recent result of [V. Colao, G. Marino, H.K. Xu, An Iterative Method for finding common solutions of equilibrium and fixed point problems, J. Math. Anal. Appl. 344 (2008) 340–352] to systems of equilibrium problems. 相似文献
30.
Gábor Elek 《Journal of Functional Analysis》2018,274(6):1657-1689
We study uniformly recurrent subgroups (URS) introduced by Glasner and Weiss [18]. Answering their query we show that any URS Z of a finitely generated group is the stability system of a minimal Z-proper action. We also show that for any sofic URS Z there is a Z-proper action admitting an invariant measure. We prove that for a URS Z all Z-proper actions admits an invariant measure if and only if Z is coamenable. In the second part of the paper we study the separable -algebras associated to URS's. We prove that if a URS is generic then its -algebra is simple. We give various examples of generic URS's with exact and nuclear -algebras and an example of a URS Z for which the associated simple -algebra is not exact and not even locally reflexive, in particular, it admits both a uniformly amenable trace and a nonuniformly amenable trace. 相似文献