Boundization, Closure and Convergence For The Ultra Extended Complex Banach and Hilbert Spaces with Applications

Abstract

Boundization, Closure and Convergence For The Ultra Extended Complex Banach and Hilbert Spaces with Applications Salah Hamad We study Boundization, Closure and Convergence of Complex Banach and Hilbert spaces. We augment a Banach space with elements "infinity" and turn the augmented set into a metric space by appropriate distance functions. This new metric space is called the Ultra Extended Banach Space. A new family of bijections, motivated by nonlinear projections, take an Ultra Extended Banach Space into bounded subsets of a "larger" Banach space. We compare the family of new metrics induced and show which ones are equivalent and which ones are unexpectedly not equivalent. Some applications are provided.