An Ordinal Index on the Space of Strictly Singular Operators

2009/08/10 by Beanland, Kevin
#03E15 #46B28 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0908.1113

Abstract

Using the notion of S_ξ-strictly singular operator introduced by Androulakis, Dodos, Sirotkin and Troitsky, we define an ordinal index on the subspace of strictly singular operators between two separable Banach spaces. In our main result, we provide a sufficient condition implying that this index is bounded by ω₁. In particular, we apply this result to study operators on totally incomparable spaces, hereditarily indecomposable spaces and spaces with few operators.

Related

• Classes of operators determined by ordinal indices
• An ordinal index characterizing weak compactness of operators
• Banach spaces of bounded Szlenk index
• Prescribed Szlenk index of separable Banch spaces
• Strictly singular operators in asymptotic ℓ_p Banach spaces