{"id":{"repo_id":"mississippi","oai_identifier":"oai:egrove.olemiss.edu:etd-2441"},"canonical_url":"https://search.dev.ndltd.org/etd/mississippi/oai:egrove.olemiss.edu:etd-2441","repository":{"repo_id":"mississippi","name":"University of Mississippi","base_url":"https://egrove.olemiss.edu/do/oai/"},"display":{"title":"Diagonals of Tensor Products of Banach Lattices with Bases.","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Lee, Byunghoon"],"institution":null,"degree_name":"Ph.D. in Mathematics","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Qingying Bu","James Cizdziel","Micah B. Milinovich"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-01T08:00:00Z","date_published":"2015-01-01T08:00:00Z","updated_at":"2026-07-24T03:06:53Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://egrove.olemiss.edu/etd/1442","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Qingying Bu","James Cizdziel","Micah B. Milinovich"]},{"key":"dc:creator","label":"Author","values":["Lee, Byunghoon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2020-01-23T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D. in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://egrove.olemiss.edu/etd/1442"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Diagonals of Tensor Products of Banach Lattices with Bases."]}]}],"canonical_facts":{"dc:contributor":["Qingying Bu","James Cizdziel","Micah B. Milinovich"],"dc:creator":["Lee, Byunghoon"],"dc:date.available":["2020-01-23T08:00:00Z"],"dc:description.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."],"dc:identifier":["https://egrove.olemiss.edu/etd/1442"],"dc:subject":["Mathematics"],"dc:title":["Diagonals of Tensor Products of Banach Lattices with Bases."],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D. in Mathematics"]},"updated_at":"2026-07-24T03:06:53Z"}