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arXiv · 1808.01823

Rank in Banach Algebras: A Generalized Cayley-Hamilton Theorem

Gareth Braatvedt·Rudi Brits·Francois Schulz
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Abstract

Let $A$ be a semisimple Banach algebra with non-trivial, and possibly infinite-dimensional socle. Addressing a problem raised by Harte and Hernandez, 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.

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Gareth Braatvedt, Rudi Brits, Francois Schulz. 2018-08-06. Rank in Banach Algebras: A Generalized Cayley-Hamilton Theorem. https://arxiv.org/abs/1808.01823

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