On operators with rational resolvent
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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Keywords: Bounded linear operator, rational resolvent, Caradus class, pole of the resolvent, spectrum, minimal equation theorem
Article copyright: © Copyright 1972 American Mathematical Society