Some questions on Tauberian operators acting on abstract $L_{1}$ spaces

• Grant number: 14/25479-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: March 30, 2015
• End date: April 29, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Eloi Medina Galego
• Grantee: Eloi Medina Galego
• Visiting researcher: Manuel Gonzalez Ortiz
• Visiting researcher institution: Universidad de Cantabria (UC), Spain
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we study tauberian operators from an abstract $L_1$-space $X$ into a Banach space $Y$. Our first objective is to obtain characterizations of these operators. Then for $X=Y$ we investigate the existence of operators of this kind with infinite dimensional kernel and/or closed range, and for $X=Y=L_1(G)$ (a convolution algebra) we try to show that every tauberian multiplier is Fredholm. (AU)