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Article Dans Une Revue Journal of Operator Theory Année : 2021

Ell-1 contractive maps on noncommutative Lp-spaces

ℓ1-contractive maps on noncommutative Lp-spaces

Résumé

Let T:Lp(M)→Lp(N) be a bounded operator between two noncommutative Lp-spaces, 1⩽p<∞. We say that T is ℓ1-bounded (respectively ℓ1-contractive) if T⊗Iℓ1 extends to a bounded (respectively contractive) map from Lp(M;ℓ1) into Lp(N;ℓ1). We show that Yeadon's factorization theorem for Lp-isometries, 1⩽p≠2<∞, applies to an isometry T:L2(M)→L2(N) if and only if T is ℓ1-contractive. We also show that a contractive operator T:Lp(M)→Lp(N) is automatically ℓ1-contractive if it satisfies one of the following two conditions: either T is 2-positive; or T is separating, that is, for any disjoint a,b∈Lp(M) (i.e.\ a∗b=ab∗=0), the images T(a),T(b) are disjoint as well.
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Dates et versions

hal-03525949 , version 1 (29-05-2024)

Identifiants

Citer

Christian Le Merdy, Safoura Zadeh. Ell-1 contractive maps on noncommutative Lp-spaces. Journal of Operator Theory, 2021, 85 (2), pp.417-442. ⟨10.7900/jot.2019oct09.2257⟩. ⟨hal-03525949⟩
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