An Ordinal Index on the Space of Strictly Singular Operators

Details An Ordinal Index on the Space of Strictly Singular Operators An Ordinal Index on the Space of Strictly Singular Operators

2009-08-10

arxiv.org/abs/0908.1113v1

Mathematics

Functional Analysis

8 pages

Scientific paper

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.

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