J-ISOMETRIC AND J-UNITARY DILATIONS OF OPERATOR KNOT
Using the term of the operator knot, the J-unitary dilation of an arbitrary bounded operator has been constructed. Along with the open system construction has been used. This paper provides a direct proof that the operator, built by the knot, is the J -unitary dilation of the main operator of the knot and its minimality. The J -isometric dilation is built preliminarily and some of its properties are proved.