DMS Graduate Student Seminar

Speaker:  Geraldo Soares de Souza, Emeritus Professor of Mathematics, Auburn University

Title: Revisiting norms and duality in $R^n$

Abstract: In this talk, we review some aspects of the norm and equivalence of norms in $R^n$ the famous Cauchy-Schwarz inequality and a “new one,” the Riesz representation theorem, and some other properties. We focus on the pathological case of $L^p$ norms for $0 < p < 1$ and introduce a new class of functions and the notion of almost e-type norm.

What is the real meaning of equivalence of norms in $R^n$?  What is the importance of this equivalence?