Publisher DOI: 10.1016/j.jmaa.2015.11.060
Title: Essential pseudospectra and essential norms of band-dominated operators
Language: English
Authors: Hagger, Raffael 
Lindner, Marko  
Seidel, Markus 
Keywords: Band-dominated operator; Essential spectrum; Fredholm theory; Limit operator; Pseudospectra
Issue Date: 1-May-2016
Source: Journal of Mathematical Analysis and Applications 1 (437): 255-291 (2016-05-01)
Abstract (english): 
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 p∈(1, ∞) and/or vector-valued lp-spaces.
URI: http://hdl.handle.net/11420/5948
ISSN: 1096-0813
Journal: Journal of mathematical analysis and applications 
Institute: Mathematik E-10 
Document Type: Article
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