Functional calculus and topological K-theory
The difference between algebraic and topological K-theory has its roots in analysis: K0 behaves like topological K-theory as long as certain tools of functional analysis apply. A central issue is the holomorphic functional calculus, which underlies several important approximation lemmas in K-theory. We shall do functional analysis using bornologies instead of topologies. We prefer bornologies because bornological algebras are very close to Banach algebras and hence provide a very natural setting for the functional calculus.
KeywordsBanach Space Exact Sequence Spectral Radius Topological Vector Space Functional Calculus
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