Компактные операторы Ганкеля над компактными Абелевыми группами

Abstract

We consider compact and connected Abelian group G with a linearly ordered dual. Based on the description of the structure of compact Hankel operators over G, generalizations of the classical Kronecker, Hartman, Peller and Adamyan - Arov - Krein theorems are obtained. A generalization of Burling’s invariant subspace theorem is also established. Applications are given to Hankel operators over discrete groups.