Strictly (co)singular operators, the Meyer-König Zeller property, and sums of Banach spaces
The author studies the following two properties a subspace Y of a Banach space Z may have: (1) If X is a subspace of Z for which \(X+Y=Z\), then \(X=Z.\) (2) If \(W\subset X\), a Banach space containing Z, then \(W\cap Z\) is closed in W whenever \(W\cap Z\subset Y.\) Results relating (1) to strictly cosingular operators and (2) to strictly singular operators are given. From these several known results of Bennett, Meyer-König, and the author which were originally proved by other methods are derived.
scientific article; zbMATH DE number 4080146