## Optimal Weyl inequality in Banach spaces

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- Proc. Amer. Math. Soc.
**134**(2006), 731-735 Request permission

## Abstract:

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.## References

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## Additional Information

**Aicke Hinrichs**- Affiliation: Mathematisches Institut, FSU Jena, Ernst-Abbe-Platz 1-3, D-07743 Jena, Germany
- Email: hinrichs@minet.uni-jena.de
- 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.
- 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: https://doi.org/10.1090/S0002-9939-05-08019-6
- MathSciNet review: 2180891

Dedicated: Dedicated to Professor Albrecht Pietsch on the occasion of his 70th birthday