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Automatic Continuity for Linear Functions Intertwining Continuous Linear Operators on Frechet Spaces

Published online by Cambridge University Press:  20 November 2018

Marc P. Thomas
Marc P. Thomas*
Affiliation:
University of Texas at Austin, Austin, Texas
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Many results concerning the automatic continuity of linear functions intertwining continuous linear operators on Banach spaces have been obtained, chiefly by B. E. Johnson and A. M. Sinclair [1; 2; 3; 5]. The purpose of this paper is essentially to extend this automatic continuity theory to the situation of Fréchet spaces. Our motive is partly to be able to handle the more general situation, since for example, questions about Fréchet spaces and LF spaces arise in connection with the functional calculus.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 3 , 01 June 1978 , pp. 518 - 530
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Johnson, B. E., Continuity of linear operators commuting with continuous linear operators, Trans. Amer. Math. Soc. 128 (1967), 88–102.Google Scholar
2. Johnson, B. E., Continuity of linear operators commuting with quasi-nilpotent operators, Indiana Math. J. 20 (1971), 913–915.Google Scholar
3. Johnson, B. E. and Sinclair, A. M., Continuity of linear operators commuting with continuous linear operators, II, Trans. Amer. Math. Soc. 146 (1969), 533–540.Google Scholar
4. Laursen, K. B., Some remarks on automatic continuity, Spaces of analytic functions, Lecture Notes in Mathematics (Springer-Yerlag, Berlin, 1976), 96–108.Google Scholar
5. Sinclair, A. M., A discontinuous intertwining operator, Trans. Amer. Math. Soc. 188 (1974), 259–267.Google Scholar
6. Sinclair, A. M. and Jewell, N. P., Epimorphisms and derivations on L1[0,1] are continuous, Bull. London Math. Soc. 8 (1976), 135–139.Google Scholar