INVARIANT BANACH LIMITS AND APPLICATIONS TO NONCOMMUTATIVE GEOMETRY
Artikel i vetenskaplig tidskrift, 2020

A linear functional B on the space of bounded sequences l(infinity) is called a Banach limit if it is positive, normalised and invariant under the shift operator. There are Banach limits which possess additional invariance properties. We prove that every Banach limit invariant under the Cesaro operator is also invariant under all dilation operators. We also prove the "continuous version" of this result and apply it to the theory of singular traces.

space of bounded sequences

Cesaro operator

dilation operator

Banach limit

Författare

Evgenii Semenov

Voronezh State University

Fedor Sukochev

University of New South Wales (UNSW)

Alexandr Usachev

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Dmitriy Zanin

University of New South Wales (UNSW)

Pacific Journal of Mathematics

0030-8730 (ISSN)

Vol. 306 1 357-373

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.2140/pjm.2020.306.357

Mer information

Senast uppdaterat

2020-12-03