Geodesic
Automatic Continuity for Linear Functions Intertwining Continuous Linear Operators on Frechet Spaces
Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 518-530

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Thomas, Marc P. Automatic Continuity for Linear Functions Intertwining Continuous Linear Operators on Frechet Spaces. Canadian journal of mathematics, Tome 30 (1978) no. 3, pp. 518-530. doi: 10.4153/CJM-1978-047-x
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[1] 1. Johnson, B. E., Continuity of linear operators commuting with continuous linear operators, Trans. Amer. Math. Soc. 128 (1967), 88–102. Google Scholar

[2] 2. Johnson, B. E., Continuity of linear operators commuting with quasi-nilpotent operators, Indiana Math. J. 20 (1971), 913–915. Google Scholar

[3] 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] 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] 5. Sinclair, A. M., A discontinuous intertwining operator, Trans. Amer. Math. Soc. 188 (1974), 259–267. Google Scholar

[6] 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

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