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) 19455844 (eISSN)
Vol. 306 1 357-373Ämneskategorier
Algebra och logik
Geometri
Matematisk analys
DOI
10.2140/pjm.2020.306.357