Wei-kai Lai

The Radon-nikodym Property for Positive Tensor Products: on the Wittstock and Fremlin Tensor Products of Orlicz Sequence Spaces and Banach Lattices Wei-kai Lai

In 1955, Grothendieck systematically introduced the general theory of tensor products for Banach spaces. As for Banach lattices case, in 1974 and 1972, Wittstock and Fremlin respectively introduced the Wittstock (positive) injective and Fremlin (positive) projective tensor product for Banach lattices. In 2006, Bu and Buskes used l_p as a special case, discussed the Radon-Nikodym property for the Wittstock and Fremlin Tensor products of l_p and Banach lattices. Based on that result, we improved the result to Orlicz sequence space, a more generalized case. In this dissertation, we first introduce several Banach lattice-valued sequence spaces. By proving they are isometrically isomorphic and Riesz isomorphic to the Wittstock injective tensor product and Fremlin projective tensor product respectively, we then use them as the sequential representations of these two positive tensor products. Finally, by studying these sequential representations, we obtain characterizations of the Radon-Nikodym property on these two positive tensor products.