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Embeddings of finite-dimensional operator spaces into the second dual

Alvaro Arias, Timur Oikhberg (2007)

Studia Mathematica

We show that, if a a finite-dimensional operator space E is such that X contains E C-completely isomorphically whenever X** contains E completely isometrically, then E is 2 15 C 11 -completely isomorphic to Rₘ ⊕ Cₙ for some n, m ∈ ℕ ∪ 0. The converse is also true: if X** contains Rₘ ⊕ Cₙ λ-completely isomorphically, then X contains Rₘ ⊕ Cₙ (2λ + ε)-completely isomorphically for any ε > 0.

Equivalences involving (p,q)-multi-norms

Oscar Blasco, H. G. Dales, Hung Le Pham (2014)

Studia Mathematica

We consider (p,q)-multi-norms and standard t-multi-norms based on Banach spaces of the form L r ( Ω ) , and resolve some question about the mutual equivalence of two such multi-norms. We introduce a new multi-norm, called the [p,q]-concave multi-norm, and relate it to the standard t-multi-norm.

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