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 $\nu$-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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