A complete locally convex space of countable dimension admitting an operator with no invariant subspaces

2010/09/14 by Stanislav Shkarin, Shkarin, Stanislav · 1 citation
Mathematics · #47A16 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47A16

paper · pdf · doi:10.48550/arxiv.1009.2644

arxiv created 2010/09/14 · arxiv updated 2010/09/15

Abstract

We construct a complete locally convex topological vector space X of countable algebraic dimension and a continuous linear operator T:X→ X such that T has no non-trivial closed invariant subspaces.

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