Resumen de Unconditional bases in tensor products of Hilbert spaces

D. Perez-Garcia

• We prove that a tensor norm α (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if ℓ2⊗⋯⊗ℓ2, 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.