Abstract: | Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove
that every symmetric tensor of unit norm in H ^(?)] s,psH{H \hat{\otimes} _{s,\pi _{s}}H} is an infinite absolute convex combination of points of the form x?x{x\otimes x} with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit
ball of H ^(?)] s,psH{H \hat{\otimes} _{s,\pi _{s}}H} . |