Abstract
The stability of an approximating sequence (An) for an operator A usually requires, besides invertibility of A, the invertibility of further operators, say B,C,…, that are well-associated to the sequence (An). We study this set, {A,B,C,…}, of so-called stability indicators of (An) and connect it to the asymptotics of ‖An‖, ‖An−1‖ and κ(An)=‖An‖‖An−1‖ as well as to spectral pollution by showing that limsupSpecεAn=SpecεA∪SpecεB∪SpecεC∪…. We further specify, for each of ‖An‖, ‖An−1‖, κ(An) and SpecεAn, under which conditions even convergence applies.
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