For which p and is the equation true?

Two remarks concerning the equation Πp(Χ,·)=Ip(Χ,·)

“…Further information as to which ~ and p the equation Np(X,')= Ip(X,') is valid for can be found in [3,5,6] In order to formulate the basic theorem of this section, it will be convenient for us to introduce another class of operator ideals. Namely, let ~ be a fixed Banach space.…”