7 papers
Duality of uncomplemented null-space and non-closed range and its impact on the regularization of Mazur-type operators
Jens Flemming, Bernd Hofmann
Up to now operators with uncomplemented null-space have been playing only a minor role in regularization theory for ill-posed inverse problems in Banach spaces. We show that ill-po…
A note on the Goldberg-Thorp example in light of the classification of linear ill-posed problems in Banach spaces
Bernd Hofmann, Jens Flemming
This note considers the strictly singular mapping, denoted by , from onto of an example by Goldberg and Thorp from 1963 as a typical hybrid-type operator in th…
New aspects of ill-posedness classification in Banach spaces
Jens Flemming, Bernd Hofmann
Motivated by a seminal paper of professor M. Z. Nashed published in 1987 on classification of ill-posed linear operator equations and distinguishing two types of ill-posedness in B…
Classification of ill-posedness for bounded linear operators in Banach spaces
Bernd Hofmann, Stefan Kindermann
In this article, concepts of well- and ill-posedness for linear operators in Hilbert and Banach spaces are discussed. While these concepts are well understood in Hilbert spaces, th…
Operator ordering by ill-posedness in Hilbert and Banach spaces
Stefan Kindermann, Bernd Hofmann
For operators representing ill-posed problems, an ordering by ill-posedness is proposed, where one operator is considered more ill-posed than another one if the former can be expre…
Comparing the ill-posedness for linear operators in Hilbert spaces
Peter Mathé, Bernd Hofmann
The difficulty for solving ill-posed linear operator equations in Hilbert space is reflected by the strength of ill-posedness of the governing operator, and the inherent solution s…