Basic properties of p-Banach spaces

In this thesis we recall the notion of a quasi-norm and a p-norm. We mention the Aoki-Rolewicz theorem which connects these two notions. We deal with generalizations of selected results from Banach spaces to p-Banach spaces for 0 < p ≤ 1. We study the class of Lp(µ) spaces. Namely, we explore their basic properties, their dual spaces and nonlinear structure.