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Essential pseudospectra and essential norms of band-dominated operators
Publikationstyp
Journal Article
Publikationsdatum
2016-05-01
Sprache
English
Institut
TORE-URI
Volume
437
Issue
1
Start Page
255
End Page
291
Citation
Journal of Mathematical Analysis and Applications 1 (437): 255-291 (2016-05-01)
Publisher DOI
Scopus ID
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.
Schlagworte
Band-dominated operator
Essential spectrum
Fredholm theory
Limit operator
Pseudospectra