2022/06/08 by Olavi Nevanlinna, Nevanlinna, Olavi
Computer Science · Mathematics · #47- 02 #47A55 #47A60 #47B99 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2206.03751
openalex publication_date 2022/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.