Infinite matrices with “few” non-zero entries and without non-trivial invariant subspaces |
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Authors: | Gleb Sirotkin |
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Institution: | Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA |
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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. |
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Keywords: | Operator Invariant subspace Transitive operator |
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