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Bulletin of the London Mathematical Society Advance Access originally published online on March 17, 2009
Bulletin of the London Mathematical Society 2009 41(2):332-340; doi:10.1112/blms/bdp007
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© 2009 London Mathematical Society

On s-numbers and Weyl inequalities of operators in Banach spaces

Bernd Carl and Aicke Hinrichs

Mathematisches Institut
FSU Jena
Ernst-Abbe-Platz 1-3
D-07743 Jena
Germany
carl@minet.uni-jena.de

Received 22 April 2008. Revision received 5 November 2008.

Let s = (sn) be an injective s-number sequence in the sense of Pietsch. We show the following Weyl inequality between geometric means of eigenvalues and s-numbers for a Riesz-operator T: X -> X acting on a (complex) Banach space of weak type 2: for any 0 < {delta} ≤ 1 and all n isin N, we have Formula , where wC2(X) is the weak cotype 2 constant of X, n{delta} colone [n/(1+{delta})] and c({delta}) ≤ c0 (1+1/{delta} ln (1/{delta})) with an absolute constant c0 ≥ 1.

2000 Mathematics Subject Classification 47B06, 47A75 (primary).

Research of the second author was supported by the DFG Heisenberg grant Hi 584/3-1.


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