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K-théorie des produits croisés et principe d’Oka. (K-theory of crossed products and Oka principle). (French) Zbl 0588.46041

Let \((\alpha_ t)_{t\in {\mathbb{R}}}\) be a one-parameter group of isometric automorphisms of a Banach algebra A. The algebra of the elements of A, which are holomorphic on a given neighborhood of \({\mathbb{R}}\) in \({\mathbb{C}}\) under the action of \((\alpha_ t)_{t\in {\mathbb{R}}}\) has the same K-theory as A.

MSC:

46L55 Noncommutative dynamical systems
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
46L05 General theory of \(C^*\)-algebras
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