OPERATORS SATISFYING P-ESTIMATES

• Other Authors: BYRD, JAMES STANLEY.
• Format: Others
• Subjects: Mathematics
• Online Access: http://purl.flvc.org/fsu/lib/digcoll/etd/3086113

Necessary and sufficient conditions for a positive operator to factor through a Banach lattice satisfying upper and lower estimates are presented. These conditions are then combined to give a necessary condition for a positive operator to factor through a super-reflexive Banach lattice. An example is then given to show that, in spite of the name given by Beauzamy, uniformly convexifying operators need not factor through any uniformly convex lattice. === A partial answer to a question of Pelczynski of which Frechet spaces contain conditional basic sequences is given. It is shown that a non-Schwartz Frechet space will contain a conditional basic sequence whenever the sequence of norms defining the topology satisfies upper and lower estimates. === Source: Dissertation Abstracts International, Volume: 46-06, Section: B, page: 1947. === Thesis (Ph.D.)--The Florida State University, 1985.