Биданец А. В.

J-isometric and J-unitary dilations of operator knot.

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The method of dilations is used in the study of the non-unitary operators. Herewith, the theory of the unitary dilations of the contractions has been full enough developed in the works of B. Szokefalvi-Nagy and Ch. Foyash. Further, the $J$-unitary dilation of an arbitrary bounded operator was constructed by Ch. Davis and A. V. Kuzhel.