Geodesic
Approximation properties in tensor products
Matematičeskie zametki, Tome 17 (1975) no. 3, pp. 459-466.

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For distinct classes of locally convex spaces and tensor topologies $a=\varepsilon$ and $a=\pi$ it is proved that $E\widehat\otimes_\alpha F$ has the approximation property if and only if $E$ and $F$ have this property. 
@article{MZM_1975_17_3_a12,
     author = {S. Heinrich},
     title = {Approximation properties in tensor products},
     journal = {Matemati\v{c}eskie zametki},
     pages = {459--466},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_3_a12/}
}
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S. Heinrich. Approximation properties in tensor products. Matematičeskie zametki, Tome 17 (1975) no. 3, pp. 459-466. http://geodesic.mathdoc.fr/item/MZM_1975_17_3_a12/