Rakočević, Vladimir; Zemánek, Jaroslav Lower s-numbers and their asymptotic behaviour. (English) Zbl 0695.47016 Stud. Math. 91, No. 3, 231-239 (1988). Let T be a bounded linear operator on a Banach space X, with unit ball U, and let \[ m(T)=\inf \{\| Tx\|:\quad \| x\| =1\},\quad q(T)=\sup \{\epsilon \geq 0:\quad TU\supset \epsilon U\}. \] Further, for \(r=1,2,..\). let \[ m_ r(T)=\sup \{m(T+F):\quad rank F<r\}, \]\[ q_ r(T)=\sup \{q(T+F):\quad rank F<r\}, \]\[ g_ r(T)=\max \{m_ r(T),q_ r(T)\}. \] The author studies the asymptotic behaviour of \(g_ r(T)\). The main result is as follows: If \(\omega_ r(T)\) is the r-th jumping point of the minimum index function of a semi-Fredholm operator T, then \[ | \omega_ r(T)| =\lim_{k}g_{kn+r}(T^ k)^{1/k}, \] where n is the stability index of T. Reviewer: U.Schlotterbeck Cited in 5 Documents MSC: 47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) 47A53 (Semi-) Fredholm operators; index theories Keywords:lower s-numbers; jumping point of the minimum index function of a semi- Fredholm operator PDFBibTeX XMLCite \textit{V. Rakočević} and \textit{J. Zemánek}, Stud. Math. 91, No. 3, 231--239 (1988; Zbl 0695.47016) Full Text: DOI EuDML