An application of pseudo-inverses. The analytic characteristic of T- regular points for closed operators
type: Item
instance of: scholarly article
title: An application of pseudo-inverses. The analytic characteristic of T- regular points for closed operators
zbMATH Open document ID: 0641.47001
author: Shijie Lu
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1988-01-01T00:00:00Z
review text: The author generalizes his results obtained in Chin. Ann. Math., Ser. A 1, 1988 to the closed operators case. The main result is the following. If T is a closed operator acting in a complex Hilbert space, \(\rho _{sF}(T)\) is the semi-Fredholm domain of T, then \(\lambda \in \rho _{sF}(T)\) is T-regular if and only if there exists a family of holomorphic vector functions \(\{f_ i(\mu)\}_{i\in I}\) defined in some neighborhood \(\Delta\) of \(\lambda\) such that \(\{f_ i(\mu)\}_{i\in I}\) forms a basis of ker(T-\(\mu)\) for \(\mu\) \(\in \Delta\). Thus the author explains why the continuity in the definition of T-regularity implies the analyticity in a sense. Besides, the author gives some applications of the analytic characteristic which improve the results obtained by \textit{C. Apostol} in Rev. Roum. Math. Pures Appl. 21, 155-175 (1976; Zbl 0336.47012).
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 4044502
zbMATH Keywords: closed operator
zbMATH Keywords: semi-Fredholm domain
zbMATH Keywords: T-regularity
zbMATH Keywords: analyticity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227978
OpenAlex ID: W2072841986
cites work: Q4104433
cites work: Q3666156
cites work: Complex geometry and operator theory
cites work: Q4130553
cites work: Q5660209
cites work: Q5612063
DOI: 10.2748/TMJ/1178227978
description: scientific article; zbMATH DE number 4044502