  In addition to Pisier's counterexample of a non-accessible maximal Banach
ideal, we will give a large class of maximal Banach ideals which {\it{are
accessible}}. The first step is implied by the observation that a "good
behaviour" of trace duality, which is canonically induced by conjugate operator
ideals can be extended to adjoint Banach ideals, if and only if these adjoint
ideals satisfy an accessibility condition (theorem 3.1). This observation leads
in a natural way to a characterization of accessible injective Banach ideals,
where we also recognize the appearance of the ideal of {\it{absolutely summing
operators}} (prop. 4.1). By the famous {\it{Grothendieck inequality}}, every
operator from $L_1$ to a Hilbert space is absolutely summing, and therefore our
search for such ideals will be directed towards Hilbert space factorization -
via an operator version of Grothendieck's inequality (lemma 4.2). As a
consequence,we obtain a class of injective ideals, which are
"quasi-accessible", and with the help of {\it{tensor stability}}, we improve
the corresponding norm inequalities, to get accessibility (theorem 4.1 and
4.2). In the last chapter of this paper we give applications, which are implied
by a non-trivial link of the above mentioned considerations to normed products
of operator ideals.
