Villanueva Díez, IgnacioPérez García, David2023-06-202023-06-2020050025-5521https://hdl.handle.net/20.500.14352/49597We prove that a tensor norm alpha (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if l(2) circle times(...)circle times l(2), endowed with the norm alpha, has an unconditional basis. This extends a classical result of Kwapien and Pelczynski. The symmetric version of that statement follows, and this extends a recent result of Defant, Diaz, Garcia and Maestre.engjournal articlehttp://www.mscand.dk/open access517.98Banach-spacesPolynomialsFormsHilbert-Schmidt operatorsUnconditional basisTensor productsP-summing operatorsMultilinear operatorsAnálisis funcional y teoría de operadores