Abstract
In this paper, we introduce two classes of localized integral operators on L 2 ( R d ) with the Wiener class W and the Kurbatov class K of integral operators as their models. We show that those two classes of localized integral operators are pseudo-inverse closed non-unital subalgebra of B 2 , the Banach algebra of all bounded operators on L 2 ( R d ) with usual operator norm.
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