We show that the Taylor (resp. Bochnak) complexification of the injective (projective) tensor product of any two real Banach spaces is isometrically isomorphic to the injective (projective) tensor product of the Taylor (Bochnak) complexifications of the two spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-2-2, author = {Gusti van Zyl}, title = {Complexification of the projective and injective tensor products}, journal = {Studia Mathematica}, volume = {187}, year = {2008}, pages = {105-112}, zbl = {1167.46017}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-2-2} }
Gusti van Zyl. Complexification of the projective and injective tensor products. Studia Mathematica, Tome 187 (2008) pp. 105-112. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-2-2/