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