Optimal Weyl-type Inequalities for Operators in Banach Spaces |
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Authors: | Bernd Carl Aicke Hinrichs |
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Institution: | (1) Department of Mathematics, Friedrich-Schiller-University Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany |
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Abstract: | Let (sn) be an s-number sequence. We show for each k = 1, 2, . . . and n ≥ k + 1 the inequality between the eigenvalues and s-numbers of a compact operator T in a Banach space. Furthermore, the constant (k + 1)1/2 is optimal for n = k + 1 and k = 1, 2, . . .. This inequality seems to be an appropriate tool for estimating the first single eigenvalues. On the other
hand we prove that the Weyl numbers form a minimal multiplicative s-number sequence and by a well-known inequality between eigenvalues and Weyl numbers due to A. Pietsch they are very good
quantities for investigating the optimal asymptotic behavior of eigenvalues.
Research of the second author was supported by the DFG Emmy-Noether grant Hi 584/2-3. |
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