Perturbations of Regularized Determinants of Operators in a Banach Space - Michael Gil (Journal of Mathematics)
Let be a separable Banach space with the approximation property. For an integer , let be a quasinormed ideal of compact operators in with a quasinorm , such that , where are the eigenvalues of and is a constant independent of . We suggest upper and lower bounds for the regularized determinants of operators from as well as bounds for the difference between determinants of two operators. Applications to the -summing operators, Hille-Tamarkin integral operators, Hille-Tamarkin matrices, Schatten-von Neumann operators, and Lorentz operator ideals are discussed.