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arXiv 2004.110322020-04-23math.OAmath.FA

Hyperreflexivity of the space of module homomorphisms between non-commutative $L^p$-spaces

J. Alaminos, J. Extremera, M. L. C. Godoy, A. R. Villena

英文摘要：

Let $\mathcal{M}$ be a von Neumann algebra, and let $0<p,q\le\infty$. Then the space $\Hom_\mathcal{M}(L^p(\mathcal{M}),L^q(\mathcal{M}))$ of all right $\mathcal{M}$-module homomorphisms from $L^p(\mathcal{M})$ to $L^q(\mathcal{M})$ is a reflexive subspace of the space of all continuous linear maps from $L^p(\mathcal{M})$ to $L^q(\mathcal{M})$. Further, the space $\Hom_\mathcal{M}(L^p(\mathcal{M}),L^q(\mathcal{M}))$ is hyperreflexive in each of the following cases: (i) $1\le q<p\le\infty$; (ii) $1\le p,q\le\infty$ and $\mathcal{M}$ is injective, in which case the hyperreflexivity constant is at most $8$.

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