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Automatic Continuity of Separating Linear Isomorphisms

Published online by Cambridge University Press:  20 November 2018

Krzysztof Jarosz
Krzysztof Jarosz*
Affiliation:
Institute of Mathematics, Warsaw University, 00-901 Warsaw, PKiN9p., Poland and Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, Il. 62026, U.S.A.
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Abstract

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A linear map A : C(T) → C(S) is called separating if f • g ≡ 0 implies Af • Ag = 0. We describe the general form of such maps and prove that any separating isomorphism is continuous.

Keywords

46E15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990 , pp. 139 - 144
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Abramovic, Y., Multiplicative representations of disjointness preserving operators, Indag. Math. 45 (1983), 265–279.Google Scholar
2. Abramovic, Y., Veksler, A. and Koldunov, V., On operators preserving disjointness, Soviet Math. Dokl. 20 (1979), 1089–1093.Google Scholar
3. Albrecht, E. and Neumann, M., Automatic continuity of generalized local linear operators, Manuscripta Math. 32 (1980), 263–294.Google Scholar
4. Albrecht, E. and Neumann, M., Automatic continuity for operators of local type, Lecture Notes in Mathematics 975, Springer-Verlag, 1983, 342–355.Google Scholar
5. Beckenstein, E. and Narici, L., A nonarchimedean Stone-Banach theorem, Proc. AMS, 100 (1987), 242–246.Google Scholar
6. Beckenstein, E. and Narici, L. Automatic continuity of certain linear isomorphisms, Acad. Royale de Belgique, Bull. Soc. R. Sci. Bruxelles, 73 (1987), 191–200.Google Scholar
7. Beckenstein, E. and Narici, L. and Todd, A. R., Variants of the Stone-Banach theorem, preprint.Google Scholar
8. de Pagter, B., A note on disjointness preserving operators, Proc. Amer. Math. Soc. 90 (1984), 543– 549.Google Scholar
9. Robinson, A., Non-standard Analysis, North-Holland Pub. Comp., Amsterdam-London, 1970.Google Scholar
10. Zakon, E., Remarks on the nonstandard real axis, in: Applications of Model Theory to Algebra, Analysis and Probability (ed. W. A. J. Luxemburg) Holt, Rinehard and Winston, New York, 1969.Google Scholar