This text is concerned with the Fredholm theory and stable approximation of bounded
linear operators generated by a class of infinite matrices $(a_{ij})$ that are either
banded or have certain decay properties as one goes away from the main diagonal.
The operators are studied on $\ell^p$ spaces of functions $\Z^N\to X$, where
$p\in[1,\infty]$, $N\in\N$ and $X$ is a complex Banach space. The latter means
that our matrix entries $a_{ij}$ are indexed by multiindices $i,j\in\Z^N$ and
that every $a_{ij}$ is itself a bounded linear operator on $X$. Our main focus
lies on the case $p=\infty$, where new results are derived, and it is demonstrated
in both general theory and concrete operator equations from mathematical physics
how advantage can be taken of these new $p=\infty$ results in the general case
$p\in[1,\infty]$.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-200901182 |
| Date | 23 July 2009 |
| Creators | Lindner, Marko |
| Contributors | TU Chemnitz, Fakultät für Mathematik, Prof. Dr. Albrecht Böttcher, Prof. Dr. Hermann Schulz-Baldes, Prof. Dr. Simon Chandler-Wilde |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf, text/plain, application/zip |
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