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A property of strictly singular 1-1 operators

George Androulakis·Per Enflo
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Abstract

We prove that if T is a strictly singular 1-1 operator defined on an infinite dimensional Banach space X, then for every infinite dimensional subspace Y of X there exists an infinite dimensional subspace Z of Y such that Z contains orbits of T of every finite length and the restriction of T on Z is a compact operator.

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George Androulakis, Per Enflo. 2001-12-25. A property of strictly singular 1-1 operators. https://arxiv.org/abs/math/0112274

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