Unconditional bases in tensor products of Hilbert spaces - Pérez-García, David; Villanueva, Ignacio (MATHEMATICA SCANDINAVICA, 2005)
We prove that a tensor norm $α$ (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if $\ell_2\otimes…\otimes \ell_2$, endowed with the norm $α$, has an unconditional basis. This extends a classical result of Kwapień and Pełczyński. The symmetric version of that statement follows, and this extends a recent result of Defant, Díaz, García and Maestre.