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Metric and algebraic perturbations of function algebras

Published online by Cambridge University Press:  20 January 2009

Krzysztof Jarosz
Krzysztof Jarosz
Affiliation:
Institute of MathematicsWarsaw UniversityWarsaw, Poland
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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

References

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