We study several properties of the Banach lattices L p (m) and L p w (m) of p-integrable scalar functions and weakly p-integrable scalar functions with respect to a countably additive vector measure m. The relation between these two spaces plays a fundamental role in our analysis. Mathematics Subject Classification 2000: 46G10, 46E30

We study continuity and other properties related to some kind of compactness of multiplication operators between different spaces of pth power integrable scalar functions with respect to a vector measure.

No abstract

DIAZ, A. FERNÁNDEZ, M. FLORENCIO and EJ. PAÚLABSTRÁCT. We study the posibility of lifting sorne properties, as heing a (barrelled, quasi-barrelled, bornological or ultrabornological) DF, gDF or quasí-normable space, frorn a locally convex space E te thé space S~0 (pi, E), of countably-valued and beunded (classes of pi-a.e. equal) functions frorn a zueasure space (fl,Z,p) into E.

Let ν be a σ-finite Banach-space-valued measure defined on a δ-ring. We find a wide class of measures ν for which interpolation with a parameter function of couples of Banach lattices of p-integrable and weakly p-integrable functions with respect to ν produces a Lorentz-type space. Moreover, we prove that if we interpolate between sums and intersections of them, then they still yield another Lorentz-type space closely related with the first one.L p 0 (m), L p 1 (m) θ,q = L p 0 w (m), L p 1 w (m) θ,q = L p,q ( m ), (1.2)