Geodesic
Characterization of the sets of divergence for sequences of operators with the localization property
Sbornik. Mathematics, Tome 202 (2011) no. 1, pp. 9-33

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General theorems characterizing the sets of divergence for sequences of operators with the localization property are established and then used to obtain a complete characterization of the sets of divergence for Fourier series and their Cesàro means in classical orthonormal systems. Bibliography: 28 titles.
Keywords: localization property of operators, sets of divergence, $G_{\delta\sigma}$-sets. 
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     title = {Characterization of the sets of divergence for sequences of operators with the localization property},
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G. A. Karagulyan. Characterization of the sets of divergence for sequences of operators with the localization property. Sbornik. Mathematics, Tome 202 (2011) no. 1, pp. 9-33. http://geodesic.mathdoc.fr/item/SM_2011_202_1_a1/