Embedding subspaces of $l\sp n\sb \infty$ into spaces with Schauder basis

Piotr Mankiewicz, Nicole Tomczak-Jaegermann
1993 Proceedings of the American Mathematical Society  
It is proved that for sufficiently small e > 0 and any 0 < S < 1/2 , a random n-dimensional subspace E of l^ , where TV = (1 + s)n , has the property: whenever E is embedded into any (1 + y)«-dimensional space with a basis, where y = cde , then the embedding constant exceeds c'nxl2~s .
doi:10.1090/s0002-9939-1993-1143019-4 fatcat:msdskjteurfy5aopsnnrt57dta