Abstract
We examine some connections between Banach space theory and other areas of functional analysis such as Lipschitz functions on metric spaces, operator theory and holomorphic function theory. We give an intrinsic characterization of the extreme points of the unit ball of the space of Lipschitz functions (modulo constant functions) on a metric space. We define nonlinear p-summing operators between metric spaces and prove a nonlinear version of the Pietsch Factorization Theorem. We prove that certain kinds of finite metric spaces are universally embeddable in a Banach space whose dimension is the cardinality of the metric space. We then consider nests of subspaces in Banach space. The order topology on the index set of a nest is discussed, and the method of spatial indexing by a vector; sufficient geometric conditions for the existence of indexing vectors are found. It is then shown that a continuous nest exists in any Banach space...
Farmer, Jeffrey Darrell (1992). Extensions and applications of infinite dimensional Banach space theory. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -1354089.