Let S p be the ideal of the Schatten-von Neumann operators with the norm N p. For an integer p ≥ 3 and an A ∈ S p, the inequalities of the type ||(I - A) -1det p(I - A)|| ≤ exp [a p N p p(A) + c p] are proved, where det p(I A) is the regularized determinant, I is the unit operator and a p, and b p 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.
- Schatten-von Neumann operators
- infinite matrices
- positive invertibility
- spectrum perturbations