Endomorphisms of commutative unital Banach algebras

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Moore, David (2017) Endomorphisms of commutative unital Banach algebras. PhD thesis, University of Nottingham.

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Abstract

This thesis is a collection of theorems which say something about the following question: if we know that a bounded operator on a commutative unital Banach algebra is a unital endomorphism, what can we say about its other properties? More specifically, the majority of results say something about how the spectrum of a commutative unital Banach algebra endomorphism is dependent upon the properties of the algebra on which it acts. The main result of the thesis (the subject of Chapter 3) reveals that primary ideals (that is, ideals with single point hulls) can sometimes be particularly important in questions of this type.

The thesis also contains some contributions to the Fredholm theory for bounded operators on an arbitrary complex Banach space. The second major result of the thesis is in this direction, and concerns the relationship between the essential spectrum of a bounded operator on a Banach space and those of its restrictions and quotients - `to' and `by' - closed invariant subspaces.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Feinstein, J.F.
Langley, J.K.
Subjects: Q Science > QA Mathematics > QA299 Analysis
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 39674
Depositing User: Moore, David
Date Deposited: 12 Jul 2017 04:40
Last Modified: 19 Oct 2017 17:42
URI: https://eprints.nottingham.ac.uk/id/eprint/39674

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