p -representable operators in Banach spaces

Let E and F be Banach spaces. An operator T ∈ L ( E , F ) is called p -representable if there exists a finite measure μ on the unit ball, B ( E * ) , of E * and a function g ∈ L q ( μ , F ) , 1 p + 1 q = 1 , such that T x = ∫ B ( E * ) 〈 x , x * 〉 g ( x * ) d μ ( x * ) for all x ∈ E . The object of this paper is to investigate the class of all p -representable operators. In particular, it is shown that p -representable operators form a Banach ideal which is stable under injective tensor product. A characterization via factorization through L p -spaces is given.