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A theorem of Krein revisited

Timur Oikhberg·Vladimir G. Troitsky
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Abstract

M. Krein proved in 1948 that if T is a continuous operator on a normed space leaving invariant an open cone, then its adjoint T* has an eigenvector. We present generalizations of this result as well as some applications to C*-algebras, operators on l_1, operators with invariant sets, contractions on Banach lattices, the Invariant Subspace Problem, and von Neumann algebras.

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Timur Oikhberg, Vladimir G. Troitsky. 2002-09-24. A theorem of Krein revisited. https://arxiv.org/abs/math/0209331

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