An Ordinal Index on the Space of Strictly Singular Operators

Kevin Beanland

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arXiv · 0908.1113

An Ordinal Index on the Space of Strictly Singular Operators

Kevin Beanland

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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 $ω_1$. In particular, we apply this result to study operators on totally incomparable spaces, hereditarily indecomposable spaces and spaces with few operators.

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BibTeX RIS

Kevin Beanland. 2009-08-10. An Ordinal Index on the Space of Strictly Singular Operators. https://arxiv.org/abs/0908.1113

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