On the invariance of index of semielliptical operator on the scale of anisotropic spaces

Аннотация

The paper is devoted to the questions of invariance of the index of a semielliptical operator on the scale of anisotropic spaces. A necessary and sufficient condition for the invariance of the index of a linear bounded operator on the embedded Hilbert spaces is obtained. This condition is applied to study the invariance of the index of a semielliptical operator. For a semielliptical operator a sufficient condition for the invariance of the index on the scale of anisotropic spaces is obtained.