Geodesic
Perturbation of Toeplitz operators and reflexivity
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 13 (2014).

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It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive. 
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Kliś-Garlicka, Kamila. Perturbation of Toeplitz operators and reflexivity. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 13 (2014). http://geodesic.mathdoc.fr/item/AUPCM_2014_13_a6/

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