Generic properties of lp -contractions and similar operator topologies

If X is a separable reflexive Banach space, there are several natural Polish topologies on B1pXq, the set of contraction operators on X (none of which being clearly “more natural” than the others), and hence several a priori different notions of genericityin the Baire category sense– for properties...

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Bibliographic Details
Published in:Israel journal of mathematics 2024
Main Authors: Grivaux, Sophie, Matheron, Etienne, Menet, Quentin
Format: Article
Language:English
Subjects:
Mathematics
Online Access:Get full text
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Summary:If X is a separable reflexive Banach space, there are several natural Polish topologies on B1pXq, the set of contraction operators on X (none of which being clearly “more natural” than the others), and hence several a priori different notions of genericityin the Baire category sense– for properties of contraction operators. So it makes sense to investigate to which extent the generic properties, i.e. the comeager sets, really depend on the chosen topology on B1(X)...
ISSN:0021-2172
1565-8511