On the duality of DW-compact operators and DW-DP operators

TL;DR

This paper explores the conditions under which DW-compact and DW-DP operators between Banach lattices have their properties preserved under taking adjoints, providing necessary and sufficient conditions for these dualities.

Contribution

It establishes new necessary and sufficient conditions on Banach lattices for the duality of DW-compact and DW-DP operators, and characterizes lattices where these properties are always preserved.

Findings

Identifies conditions for DW-compact operators to have DW-compact adjoints.

Provides criteria for DW-DP operators and their adjoints.

Characterizes Banach lattices with universal DW-compact adjoint property.

Abstract

We give a necessary condition and a sufficient condition on the Banach lattices E and F so that an operator from E to F is DW-compact whenever its adjoint is DW-compact. We do the same, with different conditions, for DW-DP operators. Moreover, we characterize the Banach lattices E and F for which the adjoint of every DW-compact operator from E to F is DW-compact.