On the structure of tensor norms related to \((p,\sigma)\)-absolutely continuous operators (Q1915571)

An interpolation norm on tensor products of \(p\)-integrable function spaces and Banach spaces which satisfies intermediate properties between the Bochner norm and the injective norm is defined. Substitutes of the classical Chevet-Persson-Saphar inequalities are obtained for this case. The so-called calculus of traced tensor norms (developed by A. Defant and K. Floret) is used in order to obtain a tensor product description of the tensor norm associated to the interpolated ideal of \((p, \sigma)\)-absolutely continuous operators defined by Jarchow and Matter. This operator ideal is contained in the operator ideal of absolutely continuous operators defined by Niculescu, and is closely related to the ideal of \(p\)-summing operators. As an application we find the largest tensor norm less than or equal to our interpolation norm.