Abstract
A densely closed operator N given in Hilbert space\(\mathfrak{H}\) is called formally normal if D(N)\( \subseteq \)D(N*)and ∥Nf ∥ = ∥N*f∥ for allfε D(N). In the present work the necessary and sufficient conditions for a formally normal operator, possessing a bounded inverse, to have a normal extension in the original Hilbert space are given. The result obtained is analogous to a result of M. I. Vishik [1], relating to the case of a symmetric operator [7 References].
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Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 605–614, December, 1967.
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Polyakov, V.N. A class of formally normal operators. Mathematical Notes of the Academy of Sciences of the USSR 2, 859–863 (1967). https://doi.org/10.1007/BF01473467
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DOI: https://doi.org/10.1007/BF01473467