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A result on the ideal structure of \(\mathcal L^r(X)\) for uniformly convex \(X\). (English) Zbl 1420.46022

The main result of this paper is that, within the class of uniformly convex Banach lattices, the purely atomic ones are completely characterized by the fact that every positive compact operator on them is approximable regular.

MSC:

46B28 Spaces of operators; tensor products; approximation properties
46B42 Banach lattices
47B65 Positive linear operators and order-bounded operators
47B07 Linear operators defined by compactness properties
47L10 Algebras of operators on Banach spaces and other topological linear spaces
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