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:qucosa:19165 |
| Date | 09 July 2009 |
| Creators | Lindner, Marko |
| Contributors | Böttcher, Albrecht, Schulz-Baldes, Hermann, Chandler-Wilde, Simon, Technische Universität Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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