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Some lower bound estimates for resolvents of a compact operator on an infinite-dimensional Hilbert space. (English) Zbl 1498.47014

Authors’ abstract: This paper presents some lower estimates for resolvents of a compact operator \(A\) on an infinite-dimensional Hilbert space. Usually, upper estimates for resolvents are known under suitable conditions but lower estimates are not known. These estimates enable us to calculate suitability results for approximation of a resolvent.

MSC:

47A10 Spectrum, resolvent
47B02 Operators on Hilbert spaces (general)
47B07 Linear operators defined by compactness properties
35B45 A priori estimates in context of PDEs
35A35 Theoretical approximation in context of PDEs
47G10 Integral operators
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35J61 Semilinear elliptic equations

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References:

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