论文标题
非交通$ l^p $空间之间模块同构的空间的过度反射性
Hyperreflexivity of the space of module homomorphisms between non-commutative $L^p$-spaces
论文作者
论文摘要
令$ \ mathcal {m} $为von neumann代数，让$ 0 <p，q \ le \ infty $。那么空间$ \ hom_ \ nathcal {m}（l^p（\ nathcal {m}），l^q（\ nathcal {m}）$ of All rirght $ \ nathcal {m nathcal {m} $ - 模块同源物来自$ l^p（\ nathcal {m nathcal {m} $ iis a $ to $ lilex a $ to $ lilex）所有连续线性映射的空间子空间从$ l^p（\ Mathcal {m}）$到$ l^q（\ Mathcal {m}）$。此外，空间$ \ hom_ \ mathcal {m}（l^p（\ mathcal {m}），l^q（\ mathcal {m}））$在以下每种情况下都是超反射性的： （ii）$ 1 \ le p，q \ le \ infty $和$ \ mathcal {m} $是注入性的，在这种情况下，超反射性常数最多为$ 8 $。
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 $8$.
