New convergence mode for the generalized spectrum approximation
Somia Kamouche, Hamza Guebbai
Laboratoire des MathГ©matiques AppliquГ©es et de ModГ©lisation, UniversiГ© 8 Mai 1945, Guelma, AlgГЁrie
Keywords: generalized spectrum, ОЅ-convergence, property U, spectral approximation
Abstract
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 ν-convergence used in the case of classical spectrum approximation. This new vision allows us to see the ν-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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