\(L_ \varphi\)-spaces and some related sequence spaces
Summary: In view of closed graph theorems in case of maps defined by operator- valued matrices \(L_ \varphi\)-spaces were recently introduced by two of the present authors as a generalization of separable \(FK(X)\)-spaces. In this paper we study the class of \(L_ \varphi\)-spaces and a few closely related classes of sequence spaces. It is shown that an analogue of Kalton's closed graph theorem holds for matrix mappings if we consider \(L_ \varphi\)-spaces as range spaces, and paralleling a result of Qiu we prove that the class of \(L_ \varphi\)-spaces is the best-possible choice here. As a consequence we show that for any \(L_ \varphi\)-space \(E\) every matrix domain \(E_ A\) is again an \(L_ \varphi\)-space.
maps defined by operator-valued matrices
scientific article; zbMATH DE number 627641