A discontinuous intertwining operator

Author:
Allan M. Sinclair

Journal:
Trans. Amer. Math. Soc. **188** (1974), 259-267

MSC:
Primary 47A99

MathSciNet review:
0361878

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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 .

**[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****[2]**Henri Cartan and Samuel Eilenberg,*Homological algebra*, Princeton University Press, Princeton, N. J., 1956. MR**0077480****[3]**James Dugundji,*Topology*, Allyn and Bacon, Inc., Boston, Mass., 1966. MR**0193606****[4]**B. E. Johnson,*Continuity of linear operators commuting with continuous linear operators*, Trans. Amer. Math. Soc.**128**(1967), 88–102. MR**0213894**, 10.1090/S0002-9947-1967-0213894-5**[5]**Barry Johnson,*Continuity of operators commuting with quasi-nilpotent operators*, Proceedings of an International Symposium on Operator Theory (Indiana Univ., Bloomington, Ind., 1970), 1971, pp. 913–915. MR**0407633****[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**0251564**, 10.1090/S0002-9947-1969-0251564-X**[7]**Irving Kaplansky,*Infinite abelian groups*, University of Michigan Press, Ann Arbor, 1954. MR**0065561**

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1974-0361878-2

Keywords:
Automatic continuity,
intertwining operator,
divisible subspace,
injective -module,
countable spectrum

Article copyright:
© Copyright 1974
American Mathematical Society