Universal families for conull FK spaces

Abstract

This paper considers the problem of determining a useful family of sequence spaces which is universal for conull FK \text {FK} spaces in the following sense: An FK \text {FK} space is conull if and only if it contains a member of the family. In the equivalent context of weak wedge spaces, an appropriate family of subspaces of boundedness domains m A {m_A} of matrices is shown to be universal. Most useful is the fact that the members of this family exhibit unconditional sectional convergence. The latter phenomenon is known for wedge spaces. Another family of spaces which is universal for conull spaces among semiconservative spaces is provided. The spaces are designed to simplify gliding humps arguments. Improvements are thereby obtained for some pseudoconull type theorems of Bennett and Kalton. Finally, it is shown that conull spaces must contain pseudoconull BK \text {BK} algebras.