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Essential pseudospectra and essential norms of band-dominated operators

Hagger, R., Lindner, M. and Seidel, M. (2015) Essential pseudospectra and essential norms of band-dominated operators. Journal of Mathematical Analysis and Applications, 437 (1). pp. 255-291. ISSN 0022-247X

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To link to this item DOI: 10.1016/j.jmaa.2015.11.060

Abstract/Summary

An operator A on an lp-space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. The coset of A in the Calkin algebra determines, for example, the Fredholmness of A, the Fredholm index, the essential spectrum, the essential norm and the so-called essential pseudospectrum of A. This coset can be identified with the collection of all so-called limit operators of A. It is known that this identification preserves invertibility (hence spectra). We now show that it also preserves norms and in particular resolvent norms (hence pseudospectra). In fact we work with a generalization of the ideal of compact operators, so-called P-compact operators, allowing for a more flexible framework that naturally extends to lp-spaces with ∈{1,∞} and/or vector-valued lp-spaces.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:84020
Publisher:Elsevier

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