We define 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. We obtain substitutes of the Chevet-Persson-Saphar inequalities for this case. We also use the calculus of traced tensor norms 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. As an application we find the largest tensor norm less than or equal to our interpolation norm.
@article{urn:eudml:doc:40195,
title = {On the structure of tensor norms related to (p,$\sigma$)-absolutely continuous operators.},
journal = {Collectanea Mathematica},
volume = {47},
year = {1996},
pages = {35-46},
zbl = {0852.46022},
mrnumber = {MR1387660},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40195}
}
Sánchez-Pérez, Enrique A. On the structure of tensor norms related to (p,σ)-absolutely continuous operators.. Collectanea Mathematica, Tome 47 (1996) pp. 35-46. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40195/