Polynomial as a new variable — A Banach algebra with a functional calculus

Olavi Nevanlinna*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

Given any square matrix or a bounded operator A in a Hilbert space such that p(A) is normal (or similar to normal), we construct a Banach algebra, depending on the polynomial p, for which a simple functional calculus holds. When the polynomial is of degree d, then the algebra deals with continuous ℂd-valued functions, defined on the spectrum of p(A). In particular, the calculus provides a natural approach to deal with nontrivial Jordan blocks and one does not need differentiability at such eigenvalues.

Original languageEnglish
Pages (from-to)567-592
Number of pages26
JournalOPERATORS AND MATRICES
Volume10
Issue number3
DOIs
Publication statusPublished - 1 Sep 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Functional calculus
  • Multicentric calculus
  • Polynomially normal
  • Removing Jordan blocks
  • Spectral mapping

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