法正态映射锥的有限角重构与分离

中文摘要 AI 辅助

我们针对𝓑(ℋ)与𝓑(𝓚)之间的凸正态映射锥构建了有限角框架，其基本结构假设是在有限裁剪-填充操作下具有稳定性。我们证明，每个点-超弱闭的裁剪-填充稳定锥完全由其有限维角锥确定；反之，每个相容的闭有限维角锥族都存在唯一的此类全局实现。对于不一定是点-超弱闭的裁剪-填充稳定锥，从其角锥的范数闭包进行重构可恰好得到该锥的点-超弱闭包。将该重构原理与有限维分离及Choi表示相结合，我们表明，全局锥的非成员关系总能通过有限维见证在单个有限角上检测到。我们针对完全正映射与可分解映射对该框架进行了说明；在可分解情形下，有限角见证的埃尔米特部分是PPT（正半定部分转置）的。

英文摘要

We develop a finite-corner framework for convex cones of normal maps between \(\mathcal B(\mathcal H)\) and \(\mathcal B(\mathcal K)\). The basic structural assumption is stability under finite cut--pad operations. We prove that every point-ultraweakly closed cut--pad stable cone is completely determined by its finite-dimensional corner cones, and conversely that every coherent family of closed finite-dimensional corner cones admits a unique global realization of this type. For a cut--pad stable cone that is not necessarily point-ultraweakly closed, reconstruction from the norm closures of its corner cones yields exactly its point-ultraweak closure. Combining this reconstruction principle with finite-dimensional separation and the Choi representation, we show that non-membership in a global cone is always detected on a single finite-dimensional corner by a finite-dimensional witness. We illustrate the framework for completely positive and decomposable maps; in the decomposable case, the Hermitian parts of the finite-corner witnesses are PPT.

发表机构

• University of Bojnord（博久尔德大学）
• The University of Jordan（约旦大学）
• Korea University（高丽大学）

机构由 AI 辅助整理，请以论文原文为准。