1996/04/24 by Frank Oertel, Oertel, Frank
Mathematics · #Advanced Banach Space Theory #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.FA #msc:46M05
paper · pdf · doi:10.48550/arxiv.math/9604218
arxiv created 1996/04/24 · arxiv updated 2016/09/06
In addition to Pisier's counterexample of a non-accessible maximal Banach ideal, we will give a large class of maximal Banach ideals which \itare 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 \itabsolutely summing operators (prop. 4.1). By the famous \itGrothendieck inequality, every operator from L1 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 \ittensor 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.