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Small isomorphisms between operator algebras

Published online by Cambridge University Press:  20 January 2009

Krzysztof Jarosz
Affiliation:
Institute of Mathematics, Warsaw University, Pkin, 00-901 Warsaw, Poland
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Let A and B be function algebras. The well-known Nagasawa theorem [5] states that A and B are isometric if and only if they are isomorphic in the category of Banach algebras. In [2] it was shown that this theorem is stable in the sense that if the Banach–Mazur distance between the underlying Banach spaces of A and B is close to one then these algebras are almost isomorphic, that is there exists a linear map T from A onto B such that . On the other hand one can get from Theorems 1 and 3 of [3] that the Nagasawa theorem can be extended to some operator algebras as follows:

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

REFERENCES

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4.Nagasawa, M., Isomorphisms between commutative Banach algebras with application to rings of analytic functions, Kodai Math. Sent. Rep. 11 (1959), 182188.Google Scholar