Date of Award
1-1-2015
Document Type
Dissertation
Degree Name
Ph.D. in Mathematics
Department
Mathematics
First Advisor
Qingying Bu
Second Advisor
James Cizdziel
Third Advisor
Micah B. Milinovich
Relational Format
dissertation/thesis
Abstract
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.
Recommended Citation
Lee, Byunghoon, "Diagonals of Tensor Products of Banach Lattices with Bases." (2015). Electronic Theses and Dissertations. 1442.
https://egrove.olemiss.edu/etd/1442