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Invariant Subspaces of Operators on a Hilbert Space

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Abstract

In year 2006 the author proposed an approach to the invariant subspace problem for an operator on a Hilbert space, based on projection-convex combinations in \(C^{*}\)-algebras with the unitary factorization property. In this paper, we present an operator inequality characterizing the invariant subspace of such an operator. Eight corollaries are obtained. For an operator \(C^{*}\)-algebra \(\mathcal{A}\) with a faithful trace, we give a sufficient condition of commutation for a partial isometry from \(\mathcal{A}\) with a projection onto its invariant subspace.

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REFERENCES

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Funding

Research was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project 1.13556.2019/13.1.

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Correspondence to A. M. Bikchentaev.

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(Submitted by S. A. Grigoryan)

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Bikchentaev, A.M. Invariant Subspaces of Operators on a Hilbert Space. Lobachevskii J Math 41, 613–616 (2020). https://doi.org/10.1134/S1995080220040058

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  • DOI: https://doi.org/10.1134/S1995080220040058

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