Hilbert Q-modules and Nuclear Ideals in the Category of V-semilattices with a Duality

AbstractThe basics of the theory of Hilbert Q-modules are established. Using this approach to V-semilattices with a duality i.e. Hilbert 2-modules, we describe a nuclear traced ideal and characterize nuclear maps in the respective category.We want to thank here the anonymous referee for many valuable and perceptive comments that allow highly improve the final version of this paper. Paul Taylor's diagram macros are acknowledged