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On the nonnegativity of operator products

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A bounded, not necessarily everywhere defined, nonnegative operator A in a Hilbert space <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\mathfrak{H}$ is assumed to intertwine in a certain sense two bounded everywhere defined operators B and C. If the range of A is provided with a natural inner product then the operators B and C induce two new operators on the completion space. This construction is used to show the existence of selfadjoint and nonnegative extensions of B*A and C*A.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland

    Seppo Hassi

  2. Department of Applied Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/C 1117 Budapest

    Zoltán Sebestyén

  3. Department of Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 av Groningen, Nederland

    Henk de Snoo

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  1. Seppo Hassi
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  2. Zoltán Sebestyén
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  3. Henk de Snoo
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Hassi, S., Sebestyén, Z. & de Snoo, H. On the nonnegativity of operator products. Acta Math Hung 109, 1–14 (2005). https://doi.org/10.1007/s10474-005-0231-x

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  • DOI: https://doi.org/10.1007/s10474-005-0231-x

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