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Transactions of the American Mathematical Society
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
MathSciNet review: 0361878
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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$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0361878-2
PII: S 0002-9947(1974)0361878-2
Keywords: Automatic continuity, intertwining operator, divisible subspace, injective $ {\text{C}}[x]$-module, countable spectrum
Article copyright: © Copyright 1974 American Mathematical Society