Unconditional bases in tensor products of Hilbert spaces

• Autores: D. Perez-Garcia
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 96, Nº 2, 2005, págs. 280-288
• Idioma: inglés
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• Resumen

  • 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.