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On some cross-norms on tensor products of ordered Banach spaces. (Russian) Zbl 1051.46054
By using the property of tensor products that allows to consider vector spaces of bilinear mappings as vector spaces of linear mappings, the author establishes the isometry of the Banach spaces of operators \({\mathcal L}_{\ell,m}(E\overline{\otimes}_kF,G^*)\) and \({\mathcal L}_{\ell,m}(E,{\mathcal L}_{\ell,m}(G,G^*))\), from which the associativity of the tensor products \((E\otimes_kF)\otimes_kG\) and \(E\otimes_k(F\otimes_kG)\) of ordered Banach spaces with a cross-norm \(k\) follows.
MSC:
46M05 Tensor products in functional analysis
46B28 Spaces of operators; tensor products; approximation properties
46B40 Ordered normed spaces
47L05 Linear spaces of operators
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