Geodesic
Approximation properties $\mathrm{AP}_s$ and $p$-nuclear operators (the case where $0$)
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 28, Tome 270 (2000), pp. 277-291 
O. I. Reinov. Approximation properties $\mathrm{AP}_s$ and $p$-nuclear operators (the case where $0
@article{ZNSL_2000_270_a12,
     author = {O. I. Reinov},
     title = {Approximation properties $\mathrm{AP}_s$ and $p$-nuclear operators (the case where $0<s<1$)},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {277--291},
     year = {2000},
     volume = {270},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a12/}
}
TY  - JOUR
AU  - O. I. Reinov
TI  - Approximation properties $\mathrm{AP}_s$ and $p$-nuclear operators (the case where $0
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2000
SP  - 277
EP  - 291
VL  - 270
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a12/
LA  - ru
ID  - ZNSL_2000_270_a12
ER  - 
%0 Journal Article
%A O. I. Reinov
%T Approximation properties $\mathrm{AP}_s$ and $p$-nuclear operators (the case where $0
%J Zapiski Nauchnykh Seminarov POMI
%D 2000
%P 277-291
%V 270
%U http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a12/
%G ru
%F ZNSL_2000_270_a12

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Among other things, it is shown that there exist Banach spaces $Z$ and $W$ such that $Z^{**}$ and $W$ have bases, and for every $p\in[1,2)$ there is an operator $T\colon W\to Z$ that is not $p$-nuclear but $T^{**}$ is $p$-nuclear.