Property (T), finite-dimensional representations, and generic representations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00498908" target="_blank" >RIV/67985840:_____/19:00498908 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1515/jgth-2018-0030" target="_blank" >http://dx.doi.org/10.1515/jgth-2018-0030</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/jgth-2018-0030" target="_blank" >10.1515/jgth-2018-0030</a>

Result language

angličtina

Original language name

Property (T), finite-dimensional representations, and generic representations

Original language description

Let G be a discrete group with Property (T). It is a standard fact that, in a unitary representation of G on a Hilbert space H {mathcal{H}}, almost invariant vectors are close to invariant vectors, in a quantitative way. We begin by showing that, if a unitary representation has some vector whose coefficient function is close to a coefficient function of some finite-dimensional unitary representation σ, then the vector is close to a sub-representation isomorphic to σ: this makes quantitative a result of P. S. Wang. We use that to give a new proof of a result by D. Kerr, H. Li and M. Pichot, that a group G with Property (T) and such that C ∗(G) {C^{∗}(G)} is residually finite-dimensional, admits a unitary representation which is generic (i.e. the orbit of this representation in Rep(G, H) {Rep(G,mathcal{H})} under the unitary group U(H) {U(mathcal{H})} is comeager). We also show that, under the same assumptions, the set of representations equivalent to a Koopman representation is comeager in Rep(G, H) {mathrm{Rep}(G,mathcal{H})}.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/GF16-34860L" target="_blank" >GF16-34860L: Logic and Topology in Banach spaces</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Group Theory

ISSN

1433-5883

e-ISSN

—

Volume of the periodical

22

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

13

Pages from-to

1-13

UT code for WoS article

000454602000001

EID of the result in the Scopus database

2-s2.0-85052713220