Noncommutative Spaces and Algebras of Functions
The starting idea of noncommutative geometry is the shift from spaces to algebras of functions defined on them. In general, one has only the algebra and there is no analogue of space whatsoever. In this Chapter we shall give some general facts about algebras of (continuous) functions on (topological) spaces. In particular we shall try to make some sense of the notion of a ‘noncommutative space’.
KeywordsTopological Space Irreducible Representation Compact Operator Maximal Ideal Structure Space
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