Geodesic
New convergence mode for the generalized spectrum
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 409-416.

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In this paper, we introduce a new convergence mode to deal with the generalized spectrum approximation of two bounded operators. This new technique is obtained by extending the well-known $\nu$-convergence used in the case of classical spectrum approximation. This new vision allows us to see the $\nu$-convergence assumption as a special case of our new method compared to the hypotheses needed in old methods, those required in this paper are weaker. In addition, we prove that the property $U$ holds, which solves the spectral pollution problem arising in spectrum approximation of unbounded operator. 
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S. Kamouche; H. Guebbai. New convergence mode for the generalized spectrum. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 409-416. http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a5/

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