Examples of operators on \(C[0, 1]\) distinguishing certain operator ideals (Q882543)

The author gives explicit examples of bounded linear operators on \(C[0,1]\) which distinguish certain operator ideals (compact, absolutely summing and nuclear). More precisely, the author constructs a family of weakly compact linear operators defined on \(C[0,1]\) and identify whether or not these operators are members of the aforementioned operator ideals. The construction of each operator uses a triangular matrix of scalars \((\alpha_{ni})_{1\leq i\leq n,n\in\mathbb{N}}\), and the results obtained can inform precisely if the operator is compact, absolutely summing, or nuclear, by observing the properties \((\alpha_{ni})_{1\leq i\leq n,n\in\mathbb{N}}.\)