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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On operators with rational resolvent


Author: Anthony F. Ruston
Journal: Proc. Amer. Math. Soc. 32 (1972), 329-330
MSC: Primary 47A10
DOI: https://doi.org/10.1090/S0002-9939-1972-0301527-6
MathSciNet review: 0301527
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Abstract: It is shown that a bounded linear operator T on a complex Banach space into itself has a rational resolvent if and only if every bounded linear operator which commutes with every bounded linear operator that commutes with T can be expressed as a polynomial in T.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0301527-6
Keywords: Bounded linear operator, rational resolvent, Caradus class, pole of the resolvent, spectrum, minimal equation theorem
Article copyright: © Copyright 1972 American Mathematical Society