The present paper is a continuation of [5, 7] where a Fredholm theory for approximation sequences is proposed and some of its properties and consequences are studied. Here this theory is specified to the class of fractal approximation methods. The main result is a formula for the so-called α-number of an approximation sequence (Aₙ) which is the analogue of the kernel dimension of a Fredholm operator.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-1-5,
author = {Steffen Roch},
title = {Algebras of approximation sequences: Fredholm theory in fractal algebras},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {53-77},
zbl = {1014.46048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-1-5}
}
Steffen Roch. Algebras of approximation sequences: Fredholm theory in fractal algebras. Studia Mathematica, Tome 151 (2002) pp. 53-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-1-5/