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Perturbations of Regularized Determinants of Operators in a Banach Space

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  • Michael Gil

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.

Suggested Citation

  • Michael Gil, 2013. "Perturbations of Regularized Determinants of Operators in a Banach Space," Journal of Mathematics, Hindawi, vol. 2013, pages 1-5, December.
    • Handle: RePEc:hin:jjmath:409604
    DOI: 10.1155/2013/409604
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