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Infinite matrices with “few” non-zero entries and without non-trivial invariant subspaces
Authors:Gleb Sirotkin
Institution:Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA
Abstract:In this paper we investigate a family of infinite matrices that act on ?1. We derive a condition sufficient to guarantee that a matrix has no non-trivial closed invariant subspaces. As a result, a simplest known operator on ?1 without invariant subspaces is obtained. All entries of the matrix of the example but one are non-negative.
Keywords:Operator  Invariant subspace  Transitive operator
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