Let 1 p < ∞. We show that p⊗F X, the Fremlin projective tensor product of p with a Banach lattice X, has the Radon-Nikodym property if and only if X has the Radon-Nikodym property; and that p⊗i X, the Wittstock injective tensor product of p with a Banach lattice X, has the Radon-Nikodym property if and only if X has the Radon-Nikodym property and each positive operator from p to X is compact, where
In this paper, we first introduce a lattice decomposition and finite-dimensional lattice decomposition (FDLD) for Banach lattices. Then we show that for a Banach lattice with FDLD, the following are equivalent: (i) it has the Radon-Nikodym property; (ii) it is a KBspace; (iii) it is a Levi space; and (iv) it is a σ -Levi space. We then give a sequential representation of the Fremlin projective tensor product of an atomic Banach lattice with a Banach lattice. Using this sequential representation, we show that if one of the Banach lattices X and Y is atomic, then the Fremlin projective tensor product X⊗ F Y has the Radon-Nikodym property (or, respectively, is a KB-space) if and only if both X and Y have the Radon-Nikodym property (or, respectively, are KB-spaces).
An improved inverse gas chromatographic method involving the use of a mass-specific detector for the determination of the glass transition temperature of polymeric materials is described. The new method allows the use of several probe solutes simultaneously with an automated, closed-loop injector and stepped temperature programming. The result is a single continuous chromatogram for each probe solute over a range of temperatures encompassing the glass transition temperature, T(g). Several different methods for the exact determination of T(g) from the chromatogram were investigated, including the classical van't Hoff-type plots with retention volumes calculated from both the peak maximum and first moment values of the elution peaks. Two new methods are also proposed for the evaluation of T(g) from either the temperature dependence of the second moments of the elution peaks for probe solutes or simple inspection of the variation of elution peak height (width) with temperature. All four methods for the determination of T(g) are evaluated with three probe solutes and four different polymers, viz., poly(methyl methacrylate), poly(ethylene terephthalate), polycarbonate, and two batches of polystyrene with different molecular weights and T(g) values. Three phenomenological models were used to interpret the chromatographic retention mechanisms of the solute probes in glassy and rubbery polymers. These are (i) the classical adsorption/absorption model for glass and rubber polymers, (ii) the single absorption mechanism model, and (iii) a dual-mode model previously used to explain the sorption of gases, such as CO(2), in glassy polymers. It is concluded that no single approach is adequate to interpret the experimental results for all of the systems, although each model is adequate for some individual solute/polymer combinations.
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