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Weyl numbers and eigenvalues of abstract summing operators |
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| Authors: | Thomas Kühn Mieczys?aw Masty?o |
| Institution: | a Fakultät für Mathematik und Informatik, Mathematisches Institut, Universität Leipzig, Johannisgasse 26, D-04103 Leipzig, Germany b Faculty of Mathematics and Computer Science, Adam Mickiewicz University and Institute of Mathematics, Polish Academy of Science (Poznań branch), Umultowska 87, 61-614 Poznań, Poland |
| Abstract: | We estimate Weyl numbers and eigenvalues of operators via studying their abstract summing norms. In particular we prove estimates of these summing norms for abstract interpolation Lorentz spaces. For this we combine factorization theorems with estimates of concavity constants. Finally we apply our general eigenvalue results to integral operators with kernels of weakly singular type. We obtain asymptotically optimal estimates which extend the well-known classical results. |
| Keywords: | Operator ideal Eigenvalues Integral operators Interpolation spaces s-numbers |
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