INVARIANT BANACH LIMITS AND APPLICATIONS TO NONCOMMUTATIVE GEOMETRY
Journal article, 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
Author
Evgenii Semenov
Voronezh State University
Fedor Sukochev
University of New South Wales (UNSW)
Alexandr Usachev
Chalmers, Mathematical Sciences, Analysis and Probability Theory
University of Gothenburg
Dmitriy Zanin
University of New South Wales (UNSW)
Pacific Journal of Mathematics
0030-8730 (ISSN) 19455844 (eISSN)
Vol. 306 1 357-373Subject Categories
Algebra and Logic
Geometry
Mathematical Analysis
DOI
10.2140/pjm.2020.306.357