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External approximation of eigenvalue problems in Banach spaces. (English) Zbl 0554.65043
Betrachtet wird das Eigenwertproblem \(Tx=\lambda x\) für lineare beschränkte Operatoren im Banach-Raum. Das Problem wird approximiert durch Eigenwertprobleme mit den Operatoren \(\{T_ h\}\). Dabei können die Näherungsoperatoren \(T_ h\) sowohl auf Teilräumen von X als auch auf Räumen definiert sein, die X umfassen. Damit ist es möglich, z. B. die Aronszajn-Methode im gleichen Rahmen zu untersuchen. Es werden hinreichende Bedingungen für die Stabilität und die starke Stabilität von \(\{T_ h\}\) angegeben.
Reviewer: W.Richert

MSC:
65J10 Numerical solutions to equations with linear operators
47A10 Spectrum, resolvent
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References:
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