Date of Award
Ph.D. in Mathematics
Micah B. Milinovich
In this dissertation, we investigate diagonals of tensor products of Banach lattices with bases. We first consider questions on the positive tensor products of l_p spaces. We characterize the main diagonals of the positive projective tensor product and the positive injective tensor product of l_p space. Then by using these two main diagonals, we characterize the reflexivity, the property of being Kantorovich - Banach spaces, and the property of being order continuous of n-fold positive projective and positive injective tensor products of l_p spaces. Next, we consider the diagonals of injective tensor product of Banach lattices with bases. Let E be a Banach lattice with a 1-unconditional basis. We first introduce four main diagonal spaces of Banach lattice E and we show that these four main diagonal spaces are pairwise isometrically isomorphic by using the 1-unconditionality of the tensor diagonal. We also show that the tensor diagonal is a 1-unconditional basic sequence in both n-fold injective and n-fold symmetric injective tensor product of Banach lattice E.
Lee, Byunghoon, "Diagonals of Tensor Products of Banach Lattices with Bases." (2015). Electronic Theses and Dissertations. 1442.