Perturbations of Regularized Determinants of Operators in a Banach Space

Abstract EN

Let X be a separable Banach space with the approximation property.

For an integer p≥1, let Γp be a quasinormed ideal of compact operators in X with a quasinorm NΓp, such that ∑k=1∞|λk(A)|p≤apNΓpp(A) (A∈Γp), where λk(A) are the eigenvalues of A and ap is a constant independent of A.

We suggest upper and lower bounds for the regularized determinants of operators from Γp as well as bounds for the difference between determinants of two operators.

Applications to the p-summing operators, Hille-Tamarkin integral operators, Hille-Tamarkin matrices, Schatten-von Neumann operators, and Lorentz operator ideals are discussed.