A bounded linear operator A on a Banach space X is said to be ?polynomially
Riesz?, if there exists a nonzero complex polynomial p such that the image
p(A) is Riesz. In this paper we give some characterizations of these
operators.
We introduce the class of "almost essentially Ruston elements" with respect to a homomorphism between two Banach algebras, a class intermediate between Ruston and Fredholm elements.
We explore the relationship between Kaplansky's Lemma about locally algebraic operators, a dual to Kaplansky's lemma, and non singularity for pairs of operators in the sense of Joseph L. Taylor. Kaplansky's Lemma ([7] Lemma 14;[10] Theorem 4.8;[11] (3.5)) says that, for bounded linear operators on Banach spaces, 0.1 locally algebraic =⇒ algebraic .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.