Weakly and weak^ p-convergent operators

Let p∈[1,∞]. Being motivated by weakly p-convergent and weak^ p-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly p-convergent and weak^ p-convergent operators between arbitrary locally convex spaces. Relationships between these classes of operators are given, and we show that they have ideal properties. Numerous characterizations of weakly p-convergent and weak^ p-convergent operators are given.