Abstract The article is devoted to building various dilatations of linear operators. The explicit construction of a unitary dilation of a compression operator is considered. Then the J-unitary dilatation of a bounded operator is constructed by means of the operator knot concept of a bounded linear operator. Using the Pavlov method, we construct the self-adjoint dilatation of a bounded dissipative operator. We consider spectral and translational representations of the self-adjoint dilatation of a densely defined dissipative operator with a nonempty set of regular points.Using the concept of an operator knot for a bounded operator and the Cayley transform, we introduce an operator knot for a linear operator. By means of this concept, we construct the J-self-adjoint dilatation of a densely defined operator with a regular point.We obtain conditions of isomorphism of extraneous dilations and their minimality.
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