Enclosure of the numerical range and resolvent estimates of non-selfadjoint operator functions
Axel Torshage
Umeå University, Sweden
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Abstract
In this paper we discuss the relationship between the numerical range of an extensive class of unbounded operator functions and the joint numerical range of the operator coefficients. Furthermore, we derive methods on how to find estimates of the joint numerical range. Those estimates are used to obtain explicitly computable enclosures of the numerical range of the operator function and resolvent estimates. The enclosure and upper estimate of the norm of the resolvent are optimal given the estimate of the joint numerical range.
Cite this article
Axel Torshage, Enclosure of the numerical range and resolvent estimates of non-selfadjoint operator functions. J. Spectr. Theory 10 (2020), no. 2, pp. 379–413
DOI 10.4171/JST/297