An affirmative answer to a core issue on limit operators

By Marko Lindner, Markus Seidel. 2014

58 citations recorded by the source corpus.

Abstract An operator on an l p -space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. It is known that a rich band-dominated operator is P -Fredholm (which is a generalization of the classical Fredholm property) if and only if all of its so-called limit operators are invertible and their inverses are uniformly bounded. We show that the condition on uniform boundedness is redundant in this statement.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bce668e2f58d079ba0c3ce0a3e5258749c16fdba

Citations in the corpus

• A metric approach to limit operators (2014, unknown): “Section 7 removes the uniform boundedness requirement in the Fredholmness criterion: we generalise the proof of Lindner and Seidel [9] for ZN and explain that their ‘main tool’ (proved for Z N directly) is again Property A in disguise.”