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Metric and algebraic perturbations of function algebras
Published online by Cambridge University Press: 20 January 2009
Extract
Let A and B be function algebras. We generalise the Nagasawa theorem by proving that the Banach–Mazur distance between the underlying Banach spaces of A and B, is close to one if and only if they are almost isomorphic, that is if and only if there is a linear map T from A onto B such that ∥T−1(Tf · Tg)−fg∥≦ε∥f∥∥g∥.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 3 , October 1983 , pp. 383 - 391
- Copyright
- Copyright © Edinburgh Mathematical Society 1983
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