Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis
Compositio Mathematica, Tome 42 (1980) no. 3, pp. 273-278. 
@article{CM_1980__42_3_273_0,
     author = {Bellenot, Steven F.},
     title = {Each {Schwartz} {Fr\'echet} space is a subspace of a {Schwartz} {Fr\'echet} space with an unconditional basis},
     journal = {Compositio Mathematica},
     pages = {273--278},
     publisher = {Sijthoff et Noordhoff International Publishers},
     volume = {42},
     number = {3},
     year = {1980},
     mrnumber = {607371},
     zbl = {0432.46003},
     language = {en},
     url = {http://www.numdam.org/item/CM_1980__42_3_273_0/}
}
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Bellenot, Steven F. Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis. Compositio Mathematica, Tome 42 (1980) no. 3, pp. 273-278. http://www.numdam.org/item/CM_1980__42_3_273_0/

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