Abstract
We prove that if T is a strictly singular one-to-one 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 X such that Z∩Y is infinite dimensional, Z contains orbits of T of every finite length and the restriction of T to Z is a compact operator.
Funding Statement
The research was partially supported by NSF.
Citation
George Androulakis. Per Enflo. "A property of strictly singular one-to-one operators." Ark. Mat. 41 (2) 233 - 252, October 2003. https://doi.org/10.1007/BF02390813
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