Rank in Banach algebras: A generalized Cayley–Hamilton theorem

G. Braatvedt, R. Brits, F. Schulz

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let A be a semisimple Banach algebra with non-trivial, and possibly infinite-dimensional socle. Addressing a problem raised in [5, p. 1399], we first define a characteristic polynomial for elements belonging to the socle, and we then show that a Generalized Cayley–Hamilton Theorem holds for the associated polynomial. The key arguments leading to the main result follow from the observation that a purely spectral approach to the theory of the socle carries alongside it an efficient method of dealing with relativistic problems associated with infinite-dimensional socles.

Original languageEnglish
Pages (from-to)389-398
Number of pages10
JournalLinear Algebra and Its Applications
Volume507
DOIs
Publication statusPublished - 15 Oct 2016

Keywords

  • Cayley–Hamilton theorem
  • Determinant
  • Rank
  • Socle

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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