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- Publisher
- Springer Journals
- Copyright
- 2019 Tusi Mathematical Research Group (TMRG)
- ISSN
- 2639-7390
- eISSN
- 2008-8752
- DOI
- 10.1007/s43034-019-00001-8
- Publisher site
- See Article on Publisher Site
Abstract
Abstract Let \(\mathcal {W}\) be an ideal of compact operators A in a Banach space X satisfying the condition \(N_\mathcal {W}(A)=\sum _{k=1}^{\infty }x_k(A)<\infty \), where \(x_k(A)\)\((k=1, 2, \ldots )\) are the Weyl numbers of A. It is proved that for all \(A\in \mathcal {W}\) and any regular \(\lambda \ne 0\) of A, the inequality $$\begin{aligned} \Vert \det \;(I-\lambda ^{-1}A)(\lambda I-A)^{-1}\Vert \le \frac{ c }{ |\lambda | } \exp \;\left[ \frac{ 2cN_\mathcal {W}(A) }{ |\lambda | }\right] \end{aligned}$$ is valid, where \(c=\sqrt{2e}\). Applications of this inequality to spectrum perturbations are also discussed.
Journal
Annals of Functional Analysis – Springer Journals
Published: Apr 1, 2020