Quasi-normas tensoriais e operadores associados no ambiente de classes de sequências

Abstract

In this work we introduce and study a class of quasi-norms on the tensor product of Banach spaces defined by means of the abstract environment of sequence classes. Relationships of this construction with classes of summing operators are presented from which classical results of the theory are recovered and new results are obtained. Still using the sequence classes environment, we define and study norms in the tensor product inspired by the construction of the injective norm and establish their relations with certain classes of integral type operators. With these norms, in addition to the results and examples constructed, before we present a characterization of a space of mid summable sequences and establish its dual.