Geodesic
On mutual “orthogonality” of classes of the spaces $C_p(X)$ and $L_p(Y)$
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2012), pp. 16-19
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In this article, it is proved that none of the infinitedimensional spaces $C_p(X)$, $L_p(Y)$, or a normed space $E$ can be embedded as a complementable subspace into another by a linear homeomorphism.
Keywords: space of continuous functions, linear homeomorphic embedding, complementable subspace. 
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     title = {On mutual {\textquotedblleft}orthogonality{\textquotedblright} of classes of the spaces $C_p(X)$ and~$L_p(Y)$},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
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     year = {2012},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2012_1_a2/}
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S. P. Gul'ko; V. R. Lazarev; T. E. Khmyleva. On mutual “orthogonality” of classes of the spaces $C_p(X)$ and $L_p(Y)$. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2012), pp. 16-19. http://geodesic.mathdoc.fr/item/VTGU_2012_1_a2/

[1] Arkhangelskii A. V., Topologicheskie prostranstva funktsii, Izd-vo MGU, M., 1989 | MR