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

  • Marc P. Thomas (a1)

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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.

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References

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1. Johnson, B. E., Continuity of linear operators commuting with continuous linear operators, Trans. Amer. Math. Soc. 128 (1967), 88102.
2. Johnson, B. E., Continuity of linear operators commuting with quasi-nilpotent operators, Indiana Math. J. 20 (1971), 913915.
3. Johnson, B. E. and Sinclair, A. M., Continuity of linear operators commuting with continuous linear operators, II, Trans. Amer. Math. Soc. 146 (1969), 533540.
4. Laursen, K. B., Some remarks on automatic continuity, Spaces of analytic functions, Lecture Notes in Mathematics (Springer-Yerlag, Berlin, 1976), 96108.
5. Sinclair, A. M., A discontinuous intertwining operator, Trans. Amer. Math. Soc. 188 (1974), 259267.
6. Sinclair, A. M. and Jewell, N. P., Epimorphisms and derivations on L1[0,1] are continuous, Bull. London Math. Soc. 8 (1976), 135139.
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Automatic Continuity for Linear Functions Intertwining Continuous Linear Operators on Frechet Spaces

  • Marc P. Thomas (a1)

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