Generic properties of l_p-contractions and similar operator topologies

2022/07/16 by Grivaux, Sophie, Matheron, Etienne, Menet, Quentin · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2207.07938

Abstract

If X is a separable reflexive Banach space, there are several natural Polish topologies on B(X), 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 genericity -- in 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 B(X). In this paper, we focus on ℓ_p - spaces, 1

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• A generic transformation is invertible

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