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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Optimal Weyl inequality in Banach spaces
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by Aicke Hinrichs PDF
Proc. Amer. Math. Soc. 134 (2006), 731-735 Request permission


A well-known multiplicative Weyl inequality states that the sequence of eigenvalues $(\lambda _k(T))$ and the sequence of approximation numbers $(a_k(T))$ of any compact operator $T$ in a Banach space satisfy \[ \prod _{k=1}^n |\lambda _k(T)| \le n^{n/2} \prod _{k=1}^n a_k(T)\] for all $n$. We prove here that the constant $n^{n/2}$ is optimal, which solves a longstanding problem.
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Additional Information
  • Aicke Hinrichs
  • Affiliation: Mathematisches Institut, FSU Jena, Ernst-Abbe-Platz 1-3, D-07743 Jena, Germany
  • Email:
  • Received by editor(s): October 6, 2004
  • Published electronically: July 18, 2005
  • Additional Notes: The research of the author was supported by the DFG Emmy-Noether grant Hi 584/2-3.

  • Dedicated: Dedicated to Professor Albrecht Pietsch on the occasion of his 70th birthday
  • Communicated by: N. Tomczak-Jaegermann
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 731-735
  • MSC (2000): Primary 47B10, 43A25
  • DOI:
  • MathSciNet review: 2180891