Abstract:
We gradually study i-operators on real vector spaces,
on real topological vector spaces, and on real normed spaces. Among
several things we prove the existence of real topological vector
spaces (different from the James’ Space) that are free of continuous
i-operators. We also prove that every real normed space can
be equivalently renormed to be free of norm i-operators. Examples
of spaces of continuous functions not admitting norm i-operators
and whose unit sphere is free of convex subsets with non-empty
interior relative to it are also found. Finally, we also provide some
results on a problem posed by Wenzel in [10].
