Biduals of tensor products in operator spaces

• Autorzy: Verónica Dimant , Maite Fernández-Unzueta
• Języki publikacji: EN

Abstrakty

EN

We study whether the operator space $V** \overset{α}{⊗} W**$ can be identified with a subspace of the bidual space $(V \overset{α}{⊗} W)**$, for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be weakened.

Kategorie tematyczne

• 47L22: Ideals of polynomials and of multilinear mappings
• 46M05: Tensor products
• 47L25: Operator spaces (= matricially normed spaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 230
• Numer: 2
• Strony: 165-185

Daty

wydano

2015

Twórcy

autor

Verónica Dimant

• Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, (B1644BID) Victoria, Buenos Aires, Argentina
• CONICET

autor

Maite Fernández-Unzueta

• Centro de Investigación en Matemáticas (Cimat), A.P. 402, Guanajuato, Gto., México

Identyfikatory

DOI

10.4064/sm8292-1-2016