Article

On Generalized Strong and Norm Resolvent Convergence

Gerald Teschl, Yifei Wang, Bing Xie, and Zhe Zhou

Abstract
We present a streamlined approach for generalized strong and norm convergence of self-adjoint operators in different Hilbert spaces. In particular, we establish convergence of associated (semi-)groups, (essential) spectra and spectral projections. In addition, we give some applications to Sturm-Liouville operators.

MSC2000: Primary 47A55, 47A10; Secondary 34L40, 34L05
Keywords: Norm resolvent convergence, Sturm-Liouville operators

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