Bochum, Univ., Diss., 2003. / Computerdatei im Fernzugriff.

Bochum, Univ., Diss., 2003. / Computerdatei im Fernzugriff.

Duisburg, Universiẗat, Diss., 1997.

Braunschweig, Techn. Universiẗat, Diss., 2000.

Bochum, Universiẗat, Diss., 2003.

Berlin, Humboldt-University, Diss., 2002.

Zugl.: Karlsruhe, Univ., Diss., 2009

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 $p\in[1,\infty]$.

Techn. Univ., Habil.-Schr.--Chemnitz, 2006.

Universiẗat, Diss., 2003--Bonn.