Abstract
This work deals on sufficient conditions for the spectral convergence of a sequence of linear operators. The general context is a complex separable Banach space and the pointwise limit of the sequence is a continuous linear operator which is not supposed to be compact. By spectral convergence is meant the self-range-uniform convergence of the approximate spectral projections. This implies the gap convergence of the approximate maximal invariant subspaces to those of the limit operator corresponding to a nonzero isolated eigenvalue (or a subset of close nonzero isolated eigenvalues) with finite algebraic multiplicity. Neither the exact nor the approximate eigenvalues are supposed to be semisimple.
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