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Journal of Mathematics
Volume 2013, Article ID 409604, 5 pages
http://dx.doi.org/10.1155/2013/409604
Research Article

Perturbations of Regularized Determinants of Operators in a Banach Space

Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel

Received 15 August 2012; Accepted 7 November 2012

Academic Editor: Mark J. Friedman

Copyright © 2013 Michael Gil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.