Lomonosov's Invariant Subspace Theorem for Multivalued Linear Operators

2000/08/29 by Peter Saveliev
Mathematics · #math.FA #math.GN #math.OA #msc:47A15 #msc:47A06 #msc:46A32 #msc:54C60

paper · pdf

published as Proc. Amer. Math. Soc. 131 (2003), 825-834 · 10 pages

arxiv created 2000/08/29 · arxiv updated 2009/11/30

Abstract

The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator K, i.e., TK=KT, then T has a non-trivial closed invariant subspace. We generalize this theorem for multivalued linear operators.

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