How many operators do there exist on a Banach space?

2002/08/07 by Th. Schlumprecht, Schlumprecht, Th.
Mathematics · #46B03 #46B20 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B03 #msc:46B20

paper · pdf · doi:10.48550/arxiv.math/0208055

arxiv created 2002/08/07 · arxiv updated 2009/11/30

Abstract

We present partial results to the following question: Does every infinite dimensional Banach space have an infinite dimensional subspace on which one can define an operator which is not a compact perturbation of a scalar multiplication?

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