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Mat. Sb. (N.S.), 1971, Volume 86(128), Number 2(10), Pages 299–313 (Mi msb3295)  

This article is cited in 5 scientific papers (total in 5 papers)

Analogs of Weyl inequalities and the trace theorem in Banach space

A. S. Markus, V. I. Matsaev


Abstract: 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(s_n^{-1}(A)+1)<\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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English version:
Mathematics of the USSR-Sbornik, 1971, 15:2, 299–312

Bibliographic databases:

UDC: 513.881+517.43
MSC: Primary 47B10; Secondary 46H10
Received: 02.11.1970

Citation: A. S. Markus, V. I. Matsaev, “Analogs of Weyl inequalities and the trace theorem in Banach space”, Mat. Sb. (N.S.), 86(128):2(10) (1971), 299–313; Math. USSR-Sb., 15:2 (1971), 299–312

Citation in format AMSBIB
\Bibitem{MarMat71}
\by A.~S.~Markus, V.~I.~Matsaev
\paper Analogs of Weyl inequalities and the trace theorem in Banach space
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 86(128)
\issue 2(10)
\pages 299--313
\mathnet{http://mi.mathnet.ru/msb3295}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=298460}
\zmath{https://zbmath.org/?q=an:0252.47022}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 15
\issue 2
\pages 299--312
\crossref{https://doi.org/10.1070/SM1971v015n02ABEH001546}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. L. Litvinov, “Traces of linear operators in locally convex spaces”, Funct. Anal. Appl., 13:1 (1979), 60–62  mathnet  crossref  mathscinet  zmath
    2. W.B. Johnson, H. König, B. Maurey, J.R. Retherford, “Eigenvalues of p-summing and lp-type operators in Banach spaces”, Journal of Functional Analysis, 32:3 (1979), 353  crossref
    3. Albrecht Pietsch, “Operator Ideals with a Trace”, Math Nachr, 100:1 (1981), 61  crossref  mathscinet  zmath  isi
    4. M. S. Agranovich, “Spectral Boundary Value Problems in Lipschitz Domains for Strongly Elliptic Systems in Banach Spaces $H_p^\sigma$ and $B_p^\sigma$”, Funct. Anal. Appl., 42:4 (2008), 249–267  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. M. Demuth, F. Hanauska, M. Hansmann, G. Katriel, “Estimating the number of eigenvalues of linear operators on Banach spaces”, Journal of Functional Analysis, 2014  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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