On the intersection of principal ideals in function spaces
Bulat Khabibullin, Enzhe Khabibullina
TL;DR
This paper introduces a method for constructing principal ideals in function spaces where the intersection of these ideals is not finitely generated, exploring similar issues in holomorphic function spaces.
Contribution
It presents a novel construction method for principal ideals with non-finitely generated intersections in real and holomorphic function spaces.
Findings
Constructed principal ideals with non-finitely generated intersections.
Extended the discussion to spaces of holomorphic functions.
Provided insights into the structure of ideals in function spaces.
Abstract
We give a method for constructing principal ideals in spaces of real functions whose intersection is not a finitely generated ideal. This problem is also discussed for spaces of holomorphic functions.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Meromorphic and Entire Functions