Titlebook: Spectral Mapping Theorems; A Bluffer‘s Guide Robin Harte Textbook 2023Latest edition The Editor(s) (if applicable) and The Author(s), under

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Algebra,The language of spectral theory is algebra, so we should begin with some kind of dictionary.

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Topology,The language of spectral theory may be algebra, but its environment is .. Topology on the one hand underlies geometry; for us it is more relevant that it also underlies the theory of limits and analysis.

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Topological Algebra,When the same set carries both algebraic and topological structure then it is good if they are “compatible”: this usually means that the algebraic operations are continuous.

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Several Variables,If the spectrum of a linear operator or algebra element is a subset of the complex numbers, then we may expect the spectrum of a pair of operators be a set of pairs of complex numbers.

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