Simplifying operators by polynomials
Functional Analysis
2022-06-09 v1
Abstract
We collect and organise known results and add some new ones of the following nature: if A is a bounded operator in a Hilbert or Banach space, does there exist a nonconstant polynomial p(z) such that p(A) is "simpler", "nicer" than A. The motivation for organising these is the following. Suppose a particular functional calculus is applicable to p(A) but not directly to A. Using "multicentric calculus" one can represent functions using p(z) as a new variable allowing the functional calculus to be extended to apply to A. Classes of operators considered are increasing chains like finite rank, compact , Riesz, almost algebraic, quasialgebraic, biquasitriangular, quasitriangular, bounded.
Cite
@article{arxiv.2206.03751,
title = {Simplifying operators by polynomials},
author = {Olavi Nevanlinna},
journal= {arXiv preprint arXiv:2206.03751},
year = {2022}
}