Geodesic
Criteria for the property (UWE) and the a-Weyl theorem
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 3, pp. 75-87

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In this paper, the property (UWE) and the a-Weyl theorem for bounded linear operators are studied in terms of the property of topological uniform descent. Sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space to have the property (UWE) and satisfy the a-Weyl theorem are established. In addition, new criteria for the fulfillment of the property (UWE) and the a-Weyl theorem for an operator function are discussed. As a consequence of the main theorem, results on the stability of the property (UWE) and the a-Weyl theorem are obtained.
Keywords: property (UWE), a-Weyl theorem, topological uniform descent. 
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     title = {Criteria for the property {(UWE)} and the {a-Weyl} theorem},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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Chenhui Sun; Xiaohong Cao. Criteria for the property (UWE) and the a-Weyl theorem. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 3, pp. 75-87. http://geodesic.mathdoc.fr/item/FAA_2022_56_3_a4/