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ON A CHARACTERISTIC PROPERTY OF FINITE-DIMENSIONAL BANACH SPACES*
Published online by Cambridge University Press: 10 March 2011
Abstract
This paper is inspired by a counter example of J. Kurzweil published in [5], whose intention was to demonstrate that a certain property of linear operators on finite-dimensional spaces need not be preserved in infinite dimension. We obtain a stronger result, which says that no infinite-dimensional Banach space can have the given property. Along the way, we will also derive an interesting proposition related to Dvoretzky's theorem.
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- Copyright © Glasgow Mathematical Journal Trust 2011
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