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- W4300183261 abstract "An operator $A$ 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. 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 $mathcal{P}$-compact operators, allowing for a more flexible framework that naturally extends to $l^p$-spaces with $pin{1,infty}$ and/or vector-valued $l^p$-spaces." @default.
- W4300183261 created "2022-10-03" @default.
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- W4300183261 date "2015-04-02" @default.
- W4300183261 modified "2023-09-30" @default.
- W4300183261 title "Essential pseudospectra and essential norms of band-dominated operators" @default.
- W4300183261 doi "https://doi.org/10.48550/arxiv.1504.00540" @default.
- W4300183261 hasPublicationYear "2015" @default.
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