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11.
We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R.J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtained of ?1-semigroup algebras which are approximately amenable but not amenable; using these, we show that bounded approximate contractibility need not imply sequential approximate amenability. Results are also given for Segal algebras on locally compact groups, and algebras of p-pseudo-functions on discrete groups. 相似文献
12.
We study norm convergence and summability of Fourier series in the setting of reduced twisted group C *-algebras of discrete groups. For amenable groups, Følner nets give the key to Fejér summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups. 相似文献
13.
Richard Sharp 《Geometriae Dedicata》2007,125(1):63-74
Let Γ be a convex co-compact group of isometries of a CAT(−1) space X and let Γ0 be a normal subgroup of Γ. We show that, provided Γ is a free group, a sufficient condition for Γ and Γ0 to have the same critical exponent is that Γ / Γ0 is amenable.
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14.
《Expositiones Mathematicae》2022,40(4):947-960
In this article we show that the main C*-algebras describing the canonical commutation relations of quantum physics, i.e., the Weyl and resolvent algebras, are in the class of Følner C*-algebras, a class of C*-algebras admitting a kind of finite approximations of Følner type. In particular, we show that the tracial states of the resolvent algebra are uniform locally finite dimensional. 相似文献
15.
We introduce mean dimensions for continuous actions of countable sofic groups on compact metrizable spaces. These generalize the Gromov–Lindenstrauss–Weiss mean dimensions for actions of countable amenable groups, and are useful for distinguishing continuous actions of countable sofic groups with infinite entropy. 相似文献
16.
本文给出了离散群的可数内不变平均的具体的表达式.证明了由可数内不变平均生成的向量空间的维数等于极小内不变平均的基数,并得到了内顺从群的一些新的刻划. 相似文献
17.
18.
In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions. 相似文献
19.
Nathaniel Pappas 《代数通讯》2013,41(10):4515-4527
We calculate the rank gradient and p-gradient of free products with amalgamation over an amenable subgroup and HNN extensions with an amenable associated subgroup. The notion of cost is used to compute the rank gradient of amalgamated free products and HNN extensions. For the p-gradient the Kurosh subgroup theorems for amalgamated free products and HNN extensions will be used. 相似文献
20.
Marius Dadarlat 《Journal of Functional Analysis》2005,228(2):394-418
In this paper we establish a direct connection between stable approximate unitary equivalence for *-homomorphisms and the topology of the KK-groups which avoids entirely C*-algebra extension theory and does not require nuclearity assumptions. To this purpose we show that a topology on the Kasparov groups can be defined in terms of approximate unitary equivalence for Cuntz pairs and that this topology coincides with both Pimsner's topology and the Brown-Salinas topology. We study the generalized Rørdam group , and prove that if a separable exact residually finite dimensional C*-algebra satisfies the universal coefficient theorem in KK-theory, then it embeds in the UHF algebra of type 2∞. In particular such an embedding exists for the C*-algebra of a second countable amenable locally compact maximally almost periodic group. 相似文献