Arens regularity and weakly compact operators

Abstract

We explore the relation between Arens regularity of a bilinear operator and the weak compactness of the related linear
operators. Since every bilinear operator has natural factorization through the projective tensor product a special attention is
given to Arens regularity of the tensor operator. We consider topological centers of a bilinear operator and we present a few
results related to bilinear operators which can be approximated by linear operators.