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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The distance from the Apostol spectrum


Authors: V. Kordula and V. Müller
Journal: Proc. Amer. Math. Soc. 124 (1996), 3055-3061
MSC (1991): Primary 47A10, 47A53
MathSciNet review: 1322931
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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*}


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03306-0
PII: S 0002-9939(96)03306-0
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
Article copyright: © Copyright 1996 American Mathematical Society