New proof of Naimark's theorem on the existence of nonpositive invariant subspaces for commuting families of unitary operators in Pontryagin spaces (Q749852)
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scientific article; zbMATH DE number 4173726
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New proof of Naimark's theorem on the existence of nonpositive invariant subspaces for commuting families of unitary operators in Pontryagin spaces |
scientific article; zbMATH DE number 4173726 |
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New proof of Naimark's theorem on the existence of nonpositive invariant subspaces for commuting families of unitary operators in Pontryagin spaces (English)
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1990
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In the paper we give a new and short proof of \textit{M. A. Naimark}'s theorem [Acta Sci. Math. 24, 177-189 (1963; Zbl 0115.333)] asserting that for every commuting family \({\mathcal F}\) of unitary operators in a \(\pi_ k\)-space \(\Pi_ k\) there exists a k-dimensional, nonpositive subspace invariant under \({\mathcal F}\).
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Naimark's theorem on the existence of nonpositive invariant subspaces for commuting families of unitary operators in Pontryagin spaces
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