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 language | English |
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Pages (from-to) | 389-398 |
Number of pages | 10 |
Journal | Linear Algebra and Its Applications |
Volume | 507 |
DOIs | |
Publication status | Published - 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