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Unitary operators with decomposable corners

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Abstract

We study pairs \((U,\mathcal{L}_0)\), where U is a unitary operator in \(\mathcal{H}\) and \(\mathcal{L}_0\subset \mathcal{H}\) is a closed subspace, such that

$$\begin{aligned} P_{\mathcal{L}_0}U|_{\mathcal{L}_0}:\mathcal{L}_0\rightarrow \mathcal{L}_0 \end{aligned}$$

has a singular value decomposition. Abstract characterizations of this condition are given, as well as relations to the geometry of projections and pairs of projections. Several concrete examples are examined.

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Funding

Research funded by grant PIP 2014 0525 CONICET.

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Authors and Affiliations

  1. Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, 1613, Los Polvorines, Argentina

    Esteban Andruchow

  2. Instituto Argentino de Matemática ‘Alberto P. Calderón‘, Saavedra 15, 3er. piso, 1083, Buenos Aires, Argentina

    Esteban Andruchow

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  1. Esteban Andruchow
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Correspondence to Esteban Andruchow.

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Communicated by Catalin Badea.

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Andruchow, E. Unitary operators with decomposable corners. Banach J. Math. Anal. 15, 10 (2021). https://doi.org/10.1007/s43037-020-00091-w

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  • DOI: https://doi.org/10.1007/s43037-020-00091-w

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