A discontinuous intertwining operator

Sinclair, Allan M.

doi:10.1090/S0002-9947-1974-0361878-2

A discontinuous intertwining operator
HTML articles powered by AMS MathViewer

by Allan M. Sinclair PDF

Trans. Amer. Math. Soc. 188 (1974), 259-267 Request permission

Abstract:

If T and R are continuous linear operators on Banach spaces X and Y with the spectrum of R countable, we obtain necessary and sufficient conditions on the pair T, R that imply the continuity of every linear operator S from X into Y satisfying $ST = RS$.

References

G. R. Allan, Embedding the algebra of formal power series in a Banach algebra, Proc. London Math. Soc. (3) 25 (1972), 329–340. MR 305071, DOI 10.1112/plms/s3-25.2.329
Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
B. E. Johnson, Continuity of linear operators commuting with continuous linear operators, Trans. Amer. Math. Soc. 128 (1967), 88–102. MR 213894, DOI 10.1090/S0002-9947-1967-0213894-5
Barry Johnson, Continuity of operators commuting with quasi-nilpotent operators, Indiana Univ. Math. J. 20 (1971), no. 10, 913–915. MR 407633, DOI 10.1512/iumj.1971.20.20078
B. E. Johnson and A. M. Sinclair, Continuity of linear operators commuting with continuous linear operators. II, Trans. Amer. Math. Soc. 146 (1969), 533–540. MR 251564, DOI 10.1090/S0002-9947-1969-0251564-X
Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. MR 0065561