26 citations · 36 across the 12 of their papers we have counts for
16 papers
A note on the quasi-local algebra of expander graphs
Bruno M. Braga, Ján Špakula, Alessandro Vignati
We show that the quasi-local algebra of a coarse disjoint union of expander graphs does not contain a Cartan subalgebra isomorphic to . N. Ozawa has recently shown tha…
Boundary representations of hyperbolic groups: the log-Sobolev case
Kevin Boucher, Ján Špakula
We study boundary representations of hyperbolic groups on the (compactly embedded) function space , the domain of the logarithmic L…
Sobolev spaces and uniform boundary representations
Kevin Boucher, Jan Spakula
We prove uniform boundedness of certain boundary representations on appropriate fractional Sobolev spaces with for arbitrary Gromov hyperbolic groups. These are clo…
Measured expanders
Kang Li, Ján Špakula, Jiawen Zhang
By measured graphs we mean graphs endowed with a measure on the set of vertices. In this context, we explore the relations between the appropriate Cheeger constant and Poincaré ine…
Measured asymptotic expanders and rigidity for Roe algebras
Kang Li, Ján Špakula, Jiawen Zhang
Our main result about rigidity of Roe algebras is the following: if and are metric spaces with bounded geometry such that their Roe algebras are -isomorphic, then an…
Relative commutant pictures of Roe algebras
Jan Spakula, Aaron Tikuisis
Let X be a proper metric space, which has finite asymptotic dimension in the sense of Gromov (or more generally, straight finite decomposition complexity of Dranishnikov and Zarich…
Coarse medians and Property A
Jan Spakula, Nick Wright
We prove that uniformly locally finite quasigeodesic coarse median spaces of finite rank and at most exponential growth have Property A. This offers an alternative proof of the fac…
A metric approach to limit operators
Jan Spakula, Rufus Willett
We extend the limit operator machinery of Rabinovich, Roch, and Silbermann from to (bounded geometry, strongly) discrete metric spaces. We do not assume the presence…
Strong hyperbolicity
Bogdan Nica, Jan Spakula
We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with sharp additional properties. Specifically, strongly hyperbolic spaces are Gromov hyper…
Uniform Local Amenability
Jacek Brodzki, Graham A. Niblo, Jan Spakula +2
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 l…
Maximal and reduced Roe algebras of coarsely embeddable spaces
Jan Spakula, Rufus Willett
Gong, Wang and Yu introduced a maximal, or universal, version of the Roe C*-algebra associated to a metric space. We study the relationship between this maximal Roe algebra and the…
On Rigidity of Roe algebras
Jan Spakula, Rufus Willett
Roe algebras are C*-algebras built using large-scale (or 'coarse') aspects of a metric space (X,d). In the special case that X=G is a finitely generated group and d is a word metri…
Coarse non-amenability and coarse embeddings
Goulnara Arzhantseva, Erik Guentner, Jan Spakula
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.
Non-K-exact uniform Roe C*-algebras
Jan Spakula
We prove that uniform Roe C*-algebras associated to some expander graphs coming from discrete groups with property (τ) are not K-exact. In particular, we show that this is the case…
Uniform version of Weyl-von Neumann theorem
Jan Spakula
We prove a "quantified" version of the Weyl-von Neumann theorem, more precisely, we estimate the ranks of approximants to compact operators appearing in the Voiculescu's theorem ap…
Controlled coarse homology and isoperimetric inequalities
Piotr Nowak, Jan Spakula
We study a coarse homology theory with prescribed growth conditions. For a finitely generated group G with the word length metric this homology theory turns out to be related to am…