On isometries of lp-spaces

Abstract

This project explores the isometries between certain classes of infinite dimensional generalized Euclidean spaces. More specifically, we characterize the isometries between l^p and l^q, where 1 ≤ p, q < ∞ . The linear isometries of normed spaces are defined to be a norm-preserving surjection, and we aim to characterize the isometries by first introducing fundamental concepts of functional analysis.