, Volume 11, Issue 1, pp 41–55 | Cite as

Optimal Weyl-type Inequalities for Operators in Banach Spaces



Let (s n ) be an s-number sequence. We show for each k = 1, 2, . . . and n ≥ k + 1 the inequality Open image in new window 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.


Hilbert Space Banach Space Compact Operator Approximation Number Eigenvalue Distribution 
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© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsFriedrich-Schiller-University JenaJenaGermany

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