Lomonosov's Invariant Subspace Theorem for Multivalued Linear Operators

Peter Saveliev

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Lomonosov's Invariant Subspace Theorem for Multivalued Linear Operators

Peter Saveliev

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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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BibTeX RIS

Peter Saveliev. 2000-08-29. Lomonosov's Invariant Subspace Theorem for Multivalued Linear Operators. https://arxiv.org/abs/math/0008214

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