Perturbations of Regularized Determinants of Operators in a Banach Space
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...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/409604 |
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| author | Michael Gil |
| author_facet | Michael Gil |
| author_sort | Michael Gil |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f8760d60fbd64165aea785684258b0c0 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f8760d60fbd64165aea785684258b0c02025-02-03T01:32:48ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/409604409604Perturbations of Regularized Determinants of Operators in a Banach SpaceMichael Gil0Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, IsraelLet 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.http://dx.doi.org/10.1155/2013/409604 |
| spellingShingle | Michael Gil Perturbations of Regularized Determinants of Operators in a Banach Space Journal of Mathematics |
| title | Perturbations of Regularized Determinants of Operators in a Banach Space |
| title_full | Perturbations of Regularized Determinants of Operators in a Banach Space |
| title_fullStr | Perturbations of Regularized Determinants of Operators in a Banach Space |
| title_full_unstemmed | Perturbations of Regularized Determinants of Operators in a Banach Space |
| title_short | Perturbations of Regularized Determinants of Operators in a Banach Space |
| title_sort | perturbations of regularized determinants of operators in a banach space |
| url | http://dx.doi.org/10.1155/2013/409604 |
| work_keys_str_mv | AT michaelgil perturbationsofregularizeddeterminantsofoperatorsinabanachspace |