Compressions of resolvents and maximal radius of regularity
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- by C. Badea and M. Mbekhta PDF
- Trans. Amer. Math. Soc. 351 (1999), 2949-2960 Request permission
Abstract:
Suppose that $\lambda - T$ is left invertible in $L(H)$ for all $\lambda \in \Omega$, where $\Omega$ is an open subset of the complex plane. Then an operator-valued function $L(\lambda )$ is a left resolvent of $T$ in $\Omega$ if and only if $T$ has an extension $\tilde {T}$, the resolvent of which is a dilation of $L(\lambda )$ of a particular form. Generalized resolvents exist on every open set $U$, with $\overline {U}$ included in the regular domain of $T$. This implies a formula for the maximal radius of regularity of $T$ in terms of the spectral radius of its generalized inverses. A solution to an open problem raised by J. Zemánek is obtained.References
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Additional Information
- C. Badea
- Affiliation: URA 751 au CNRS & UFR de Mathématiques, Université de Lille I, F–59655 Villeneuve d’Ascq, France
- Email: badea@gat.univ-lille1.fr
- M. Mbekhta
- Affiliation: URA 751 au CNRS & UFR de Mathématiques, Université de Lille I, F–59655 Villeneuve d’Ascq, France
- Address at time of publication: University of Galatasaray, Çiragan Cad no 102, Ortakoy 80840, Istanbul, Turkey
- MR Author ID: 121980
- Email: mbekhta@gat.univ-lille1.fr
- Received by editor(s): February 17, 1997
- Published electronically: March 8, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 2949-2960
- MSC (1991): Primary 47A10, 47A20
- DOI: https://doi.org/10.1090/S0002-9947-99-02365-X
- MathSciNet review: 1621709