Compressions of Resolvents and Maximal Radius of Regularity

Simple item page
dc.creatorBadea, C.
dc.creatorMbekhta, M.
dc.date1999-06-11
dc.date.accessioned2026-07-07T05:29:27Z
dc.date.available2026-07-07T05:29:27Z
dc.descriptionSuppose that $λ- T$ is left-invertible in $L(H)$ for all $λ\in Ω$, where $Ω$ is an open subset of the complex plane. Then an operator-valued function $L(λ)$ is a left resolvent of $T$ in $Ω$ if and only if $T$ has an extension $\tilde{T}$, the resolvent of which is a dilation of $L(λ)$ of a particular form. Generalized resolvents exist on every open set $U$, with $\bar{U}$ 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.
dc.description15 pages, to appear in Trans. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/9906072
dc.identifierhttp://arxiv.org/abs/math/9906072
dc.identifierTrans. Amer. Math. Soc. 351(1999), 2949-2960.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78644
dc.subjectFunctional Analysis
dc.subject47A10, 47A20
dc.titleCompressions of Resolvents and Maximal Radius of Regularity
dc.typetext

Files

Collections

arXiv