96 citations · 190 across the 18 of their papers we have counts for
10 papers · 1 filter
Norms of spherical averaging operators for some geometric group actions
Bogdan Nica
We obtain asymptotic estimates for the -operator norm of spherical averaging operators associated to certain geometric group actions. The motivating example is the case of…
On bounded elementary generation for over polynomial rings
Bogdan Nica
Let be the polynomial ring over a finite field . It is shown that, for , the special linear group is boundedly generated by the elementary matrices.
Two applications of strong hyperbolicity
Bogdan Nica
We present two analytic applications of the fact that a hyperbolic group can be endowed with a strongly hyperbolic metric. The first application concerns the crossed-product C*-alg…
On operator norms for hyperbolic groups
Bogdan Nica
We estimate the operator norm of radial non-negative functions on hyperbolic groups. As a consequence, we show that several forms of Haagerup's inequality are optimal.
A true relative of Suslin's normality theorem
Bogdan Nica
We prove a normality theorem for the "true" elementary subgroups of defined by the ideals of a commutative unital ring . Our result is an analogue of a normality theor…
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…
Linear groups - Malcev's theorem and Selberg's lemma
Bogdan Nica
An account of two fundamental facts concerning finitely generated linear groups: Malcev's theorem on residual finiteness, and Selberg's lemma on virtual torsion-freeness.
Proper isometric actions of hyperbolic groups on -spaces
Bogdan Nica
We show that every non-elementary hyperbolic group $\G$ admits a proper affine isometric action on $L^p(\bd\G\times \bd\G)$, where $\bd\G$ denotes the boundary of $\G$ and is l…
On the degree of rapid decay
Bogdan Nica
A finitely generated group $\G$ equipped with a word-length is said to satisfy property RD if there are such that, for all non-negative integers , we have $\|a\|\le…
Group actions on median spaces
Bogdan Nica
We investigate the geometry of median metric spaces. The group-theoretic applications are towards Kazhdan's property (T) and Haagerup's property.