Geodesic
Analogs of Weyl inequalities and the trace theorem in Banach space
Sbornik. Mathematics, Tome 15 (1971) no. 2, pp. 299-312 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $A$ be a completely continuous operator acting on the Banach space $\mathfrak B$, let $\{\lambda_j(A)\}$ be the complete system of its eigenvalues (with regard for multiplicity) and let $s_{n+1}(A)$ be the distance from $A$ to the set of all operators of range dimension not greater than $n$. If \begin{equation} \sum_{n=1}^\infty s_n(A)\ln\bigl(s_n^{-1}(A)+1\bigr)<\infty, \end{equation} then $\operatorname{sp}A=\sum\lambda_j(A)$, where $\operatorname{sp}A$ is a functional which is linear on the set of operators satisfying condition (1) (and continuous in a certain topology) and which coincides with its trace for finite-dimensional $A$. The proof of this theorem is based on certain analogs of the famous Weyl inequalities. Bibliography: 14 titles. 
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     title = {Analogs of {Weyl} inequalities and the trace theorem in {Banach} space},
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A. S. Markus; V. I. Matsaev. Analogs of Weyl inequalities and the trace theorem in Banach space. Sbornik. Mathematics, Tome 15 (1971) no. 2, pp. 299-312. http://geodesic.mathdoc.fr/item/SM_1971_15_2_a6/

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