Related papers: Some notes on property A
Property A introduced by Guoliang Yu is an amenability-type property for metric spaces. In this article, we study property A for uniformly locally finite coarse spaces. Main examples of coarse spaces are a metric space, a set equipped with…
We study property A for metric spaces $X$ with bounded geometry introduced by Guoliang Yu. Property A is an amenability-type condition, which is less restrictive than amenability for groups. The property has a connection with…
We formalize the concept of a family of metric spaces satisfying a coarse property uniformly and we generalize finite decomposition complexity of Erik Guentner, Romain Tessera, and Guoliang Yu. Of particular interest are results determining…
Property A was introduced by Yu as a non-equivariant analogue of amenability. Nigel Higson posed the question of whether there is a homological characterisation of property A. In this paper we answer Higson's question affirmatively by…
We study property A defined by G. Yu and the operator norm localization property defined by X. Chen, R. Tessera, X. Wang, and G. Yu. These are coarse geometric properties for metric spaces which have applications to operator K-theory. It is…
We characterize groups with Guoliang Yu's property A (i.e., exact groups) by the existence of a family of uniformly bounded representations which approximate the trivial representation.
We define a relative property A for a countable group with respect to a finite family of subgroups. Many characterizations for relative property A are given. In particular a relative bounded cohomological characterization shows that if a…
Recent research in coarse geometry revealed similarities between certain concepts of analysis, large scale geometry, and topology. Property A of G.Yu is the coarse analog of amenability for groups and its generalization (exact spaces) was…
Property A is a geometric property originally introduced for discrete metric spaces to provide a sufficient condition for coarse embeddability into Hilbert space, and it is defined via a F\o{}lner condition similar in spirit to the…
We construct the first example of a coarsely non-amenable (= without Guoliang Yu's property A) metric space with bounded geometry which coarsely embeds into a Hilbert space.
For locally compact groups, we define an analogue to Yu's property A that he defined for discrete metric spaces. We show that our property A for locally compact groups agrees with Roe's notion of property A for proper metric spaces, defined…
The main results of this paper show that various coarse (`large scale') geometric properties are closely related. In particular, we show that property A implies the operator norm localisation property, and thus that norms of operators…
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…
For uniformly dicrete metric spaces without bounded geometry we suggest a modified version of property A based on metrics of bounded geometry greater than the given metric. We show that this version still implies coarse embeddability in…
Geometric property (T) was defined by Willett and Yu, first for sequences of graphs and later for more general discrete spaces. Increasing sequences of graphs with geometric property (T) are expanders, and they are examples of coarse spaces…
This paper is devoted to dualization of paracompactness to the coarse category via the concept of $R$-disjointness. Property A of G.Yu can be seen as a coarse variant of amenability via partitions of unity and leads to a dualization of…
Let $X$ be a metric space with bounded geometry, $p\in\{0\} \cup [1,\infty]$, and let $E$ be a Banach space. The main result of this paper is that either if $X$ has Yu's Property A and $p\in(1,\infty)$, or without any condition on $X$ when…
In this short note, we give a complete answer to the question of when the generalised F\o lner sets exhibiting property A can be chosen to be subsets of the space itself. More precisely, we prove that this holds for any discrete metric…
We expose a class of discrete metric spaces, for which bounded geometry is equivalent to the property A of G. Yu. This class includes the coarse disjoint union of $(\mathbb Z/2\mathbb Z)^n$, $n\in\mathbb N$, and consists of spaces of simple…
In this note we study the natural question of when the generalised F{\o}lner sets exhibiting property A can be chosen to be subsets of the space itself. We show that for many property A spaces $X$, this is indeed possible. Specifically this…