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?