The distance from the Apostol spectrum
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- by V. Kordula and V. Müller PDF
- Proc. Amer. Math. Soc. 124 (1996), 3055-3061 Request permission
Abstract:
If $T$ is an s-regular operator in a Banach space (i.e. $T$ has closed range and $N(T)\subset R^{\infty }(T)$) and $\gamma (T)$ is the Kato reduced minimum modulus, then \begin{equation*}\lim _{n\to \infty }\gamma (T^{n})^{1/n}=\sup \{r: T-\lambda { \operatorname {is s-regular for }}|\lambda |<r\}. \end{equation*}References
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Additional Information
- V. Kordula
- Affiliation: Institute of Mathematics AV ČR, Žitná 25, 115 67 Praha 1, Czech Republic
- V. Müller
- Affiliation: Institute of Mathematics AV ČR, Žitná 25, 115 67 Praha 1, Czech Republic
- Email: vmuller@mbox.cesnet.cz
- Received by editor(s): October 14, 1994
- Received by editor(s) in revised form: January 26, 1995
- Additional Notes: The research was supported by the grant No. 119106 of the Academy of Sciences of the Czech Republic.
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3055-3061
- MSC (1991): Primary 47A10, 47A53
- DOI: https://doi.org/10.1090/S0002-9939-96-03306-0
- MathSciNet review: 1322931