Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A discontinuous intertwining operator


Author: Allan M. Sinclair
Journal: Trans. Amer. Math. Soc. 188 (1974), 259-267
MSC: Primary 47A99
DOI: https://doi.org/10.1090/S0002-9947-1974-0361878-2
MathSciNet review: 0361878
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] G. R. Allan, Embedding the algebra of formal power series in a Banach algebra, Proc. London Math. Soc. (3) 25 (1972), 329-340. MR 0305071 (46:4201)
  • [2] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR 17, 1040. MR 0077480 (17:1040e)
  • [3] J. Dugundji, Topology, Allyn and Bacon, Boston, Mass., 1966. MR 33 #1824. MR 0193606 (33:1824)
  • [4] B. E. Johnson, Continuity of linear operators commuting with continuous linear operators, Trans. Amer. Math. Soc. 128 (1967), 88-102. MR 35 #4748. MR 0213894 (35:4748)
  • [5] -, Continuity of operators commuting with quasi-nilpotent operators, Indiana Univ. Math. J. 20 (1971), 913-915. MR 0407633 (53:11405)
  • [6] 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 40 #4791. MR 0251564 (40:4791)
  • [7] I. Kaplansky, Infinite abelian groups, Univ. of Michigan Press, Ann Arbor, Mich., 1954. MR 16, 444. MR 0065561 (16:444g)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47A99

Retrieve articles in all journals with MSC: 47A99


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0361878-2
Keywords: Automatic continuity, intertwining operator, divisible subspace, injective $ {\text{C}}[x]$-module, countable spectrum
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society