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Item type:Publication, Access status: without files , Essential pseudospectra and essential norms of band-dominated operators(2016-05-01); ; 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.Publicationtype: Journal Article127 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , An affirmative answer to a core issue on limit operatorsAn operator on an lᵖ-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.Publicationtype: Journal Article98