非交换L^p-空间的代数张量积与内hom
Algebraic tensor products and internal homs of noncommutative L^p-spaces
摘要：
证明了乘法映射L^a（M）\otimes_M L^b（M）\to L^{a+b}（M）是（拟）Banach M-M-双模的等距同构.这里L^a（M）= L_{1/a}（M）是任意von Neumann代数M的非交换L_p-空间，\otimes_M表示M上的代数张量积，它具有（拟）投射张量范数，但没有任何完备性。类似地，左乘法映射L^a（M）\to Hom_M（L^b（M），L^{a+b}（M））是（拟）Banach M-M-双模的等距同构，其中Hom_M表示代数内hom.特别是，我们建立了一个自动连续性的结果，这样的地图。这些结果的应用包括对所有p \ge 0建立Junge和Sherman的L_p（M）-模范畴之间的显式代数等价关系，以及确定L^p-空间上的双线性型空间的子空间.
英文摘要：
We prove that the multiplication map L^a(M)\otimes_M L^b(M)\to L^{a+b}(M) is an isometric isomorphism of (quasi)Banach M-M-bimodules. Here L^a(M)=L_{1/a}(M) is the noncommutative L_p-space of an arbitrary von Neumann algebra M and \otimes_M denotes the algebraic tensor product over M equipped with the (quasi)projective tensor norm, but without any kind of completion. Similarly, the left multiplication map L^a(M)\to Hom_M(L^b(M),L^{a+b}(M)) is an isometric isomorphism of (quasi)Banach M-M-bimodules, where Hom_M denotes the algebraic internal hom. In particular, we establish an automatic continuity result for such maps. Applications of these results include establishing explicit algebraic equivalences between the categories of L_p(M)-modules of Junge and Sherman for all p\ge0, as well as identifying subspaces of the space of bilinear forms on L^p-spaces.
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