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Adjoint to each other linear relations. Nieminen type criteria

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Abstract

Assume that \({{\mathfrak {H}}}\) and \({{\mathfrak {K}}}\) are two real or complex Hilbert spaces, A a linear relation from \({{\mathfrak {H}}}\) to \({{\mathfrak {K}}}\) and B a linear relation from \({{\mathfrak {K}}}\) to \({{\mathfrak {H}}}\), respectively. Necessary and sufficient conditions for B to be equal to the adjoint of A are provided. New characterizations for closed, skew–adjoint and selfadjoint linear relations are obtained.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, “Gheorghe Asachi” Technical University of Iaşi, B-dul Carol I, nr. 11, 700506, Iaşi, Romania

    Marcel Roman & Adrian Sandovici

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  1. Marcel Roman
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  2. Adrian Sandovici
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Correspondence to Adrian Sandovici.

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Communicated by Adrian Constantin.

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Roman, M., Sandovici, A. Adjoint to each other linear relations. Nieminen type criteria. Monatsh Math 196, 191–205 (2021). https://doi.org/10.1007/s00605-021-01579-9

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  • DOI: https://doi.org/10.1007/s00605-021-01579-9

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