INEQUALITIES OF THE CARLEMAN TYPE FOR SCHATTEN-VON NEUMANN OPERATORS

Abstract

Let Sp be the ideal of the Schatten-von Neumann operators with the norm Np. For an integer p ≥ 3 and an A ∈ Sp, the inequalities of the type [Formula: see text] are proved, where detp(I – A) is the regularized determinant, I is the unit operator and ap, and bp are explicitly pointed constants. Applications of these inequalities to spectrum perturbations of operators, as well as to invertibility and positive invertibility of infinite matrices are also discussed.