A desigualdade de Grothendieck e os teoremas de Grothendieck para operadores absolutamente somantes definidos em espaços Lp

Abstract

The main result of the work is the Grothendieck inequality, developed in 1958 by the French naturalized mathematician Grothendieck. We address the definitions of sequences that are absolutely summable and unconditionally summable, the absolutely summing operators, as well as several results that develop from these definitions. As a consequence of Grothendieck’s inequality, we have Grothendieck’s theorem, which tells us that every linear and continuous operator of l1 in l2 is absolutely summing. Finally, we study the so-called p-summing operators and their properties, Lp spaces and Grothendieck’s theorem versions for absolutely summing operators defined in Lp spaces.