This is an announcement for the paper "An ordinal index on the space of strictly singular operators" by Kevin Beanland.
Abstract: Using the notion of $S_\xi$-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 $\omega_1$. In particular, we apply this result to study operators on totally incomparable spaces, hereditarily indecomposable spaces and spaces with few operators.
Archive classification: math.FA
Mathematics Subject Classification: 46B28; 03E15
Remarks: 8 pages
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Submitted from: kbeanland@gmail.com
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