On the norm bounded sets of the ideal \(E^{a}\)

The paper is devoted to study the norm bounded subsets which are contained in \(E^{a}\) $E^a$ . Also, we introduce and study the class of the bounded- \(E^a\) $E^a$ operators, which maps the closed unit ball of a Banach space to a subset of \(E^{a}\) $E^a$ . Some interesting results about this class of operators are presented.