Paracomplete normed spaces and Fredholm theory
type: Item
instance of: scholarly article
title: Paracomplete normed spaces and Fredholm theory
zbMATH Open document ID: 0943.47011
DOI: 10.1007/BF02857302
author: Teresa Álvarez
author: M. González
publication date: 2000-08-28T00:00:00Z
review text: A normed space is called paracomplete, if it admits another norm and it is complete with respect to that norm. The authors prove: A normed space \(X\) is paracomplete if and only if the algebra \(L(X)\) of all continuous linear operators acting in \(X\) is paracomplete. Consequently all operators in \(L(X)\) have compact spectra if \(X\) is paracomplete. Further the authors characterize the closed linear operators between paracomplete spaces, which are Fredholm operators, and the linear continuous operators between normed spaces, which are almost semi-Fredholm operators in the sense of R.~Harte.
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 1339484
zbMATH Keywords: generalized Fredholm operators
zbMATH Keywords: spectrum
zbMATH Keywords: paracomplete
reviewed by: K.-H. Förster
MaRDI profile type: Publication
cites work: Q3873027
cites work: On operator ranges
cites work: The fine spectrum of the Cesàro operator in \(\ell _ p(1<p<\infty)\)
cites work: Q3994350
full work available at URL: https://doi.org/10.1007/bf02857302
OpenAlex ID: W2058237049
published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 1339484