Factoring compact operators and approximable operators
Let \(E\) be a Banach space, \(F\) be an ordered Banach space which belongs to a certain class of ordered spaces (say, Banach lattices). Let \(U: E\to F\) be a compact operator. The authors search for a factorization according to the scheme \(E @> U_ 1 >> G @> U_ 2 >> F\), where \(U_ 1\), \(U_ 2\) are compact operators and \(G\) is a reflexive ordered Banach space from a class which is as close as possible to those of \(F\). A modified version of the classical Davis-Figiel-Johnson-Pelczynski scheme is used. The article contains many interesting results. I would like only to mention that both, the problem of factorization and the problem of approximability, were under consideration in the reviewer's article [Soviet Math. Dokl. 17, 423-426 (1976; Zbl 0345.46011)] which is not quoted.
scientific article; zbMATH DE number 6502