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Lindner, Marko : Removing the ''Nasty Condition'' of Limit Operator Business in the Two Extremal Lebesgue Spaces

Lindner, Marko : Removing the ''Nasty Condition'' of Limit Operator Business in the Two Extremal Lebesgue Spaces

Author(s):
Lindner, Marko
Title:
Removing the ''Nasty Condition'' of Limit Operator Business in the Two Extremal Lebesgue Spaces
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 7, 2003
Mathematics Subject Classification:
47C05 [ Operators in algebras ]
47B38 [ Operators on function spaces ]
Abstract:
Limit operators are used when the behaviour of an operator at some singular, outstanding point like $\infty$ is of interest. Typical applications are the study of Fredholmness and invertibility at infinity of an operator, but also the applicability of approximation methods. All these properties can be characterized by the invertibility of several limit operators and the uniform boundedness of their inverses. We will show that the uniform boundedness condition is redundant in the cases $L^p(\R^n)$ and $\ell^p(\Z^n)$ for $p=1$ and $p=\infty$.
Keywords:
limit operators, band operators, band-dominated operators, Fredholmness, invertibility at infinity
Language:
English
Publication time:
10 / 2003