Little Grothendieck's Theorem for real JB*-triples
We prove that given a real JB*-triple E, and a real
Hilbert space H, then the set of those bounded linear operators
T from E to H, such that there exists a norm one functional
\phi in E* and corresponding pre-Hilbertian semi-norm
|.|_\phi on E such that |T(x)| \leq 4 \sqrt{2}
|T\|.|x\|_\phi for all x in E, is norm dense in the
set of all bounded linear operators from E to H.
A. M. Peralta