UCP映射度量空间的Gromov-Hausdorff收敛性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-07-08 DOI:10.1016/j.geomphys.2025.105588

Tirthankar Bhattacharyya, Ritul Duhan, Chandan Pradhan

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引用次数: 0

摘要

证明了van Suijlekom在算子系统谱三元组上施加一组条件的技术保证了单位完全正映射（具有可度量的bw拓扑）集合序列的Gromov-Hausdorff收敛性。这意味着，即使只有狄拉克算子的一部分谱和C -代数的某个截断是可用的，也可以提取有关几何的信息。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Gromov-Hausdorff convergence of metric spaces of UCP maps

It is shown that van Suijlekom's technique of imposing a set of conditions on operator system spectral triples ensures Gromov-Hausdorff convergence of sequences of sets of unital completely positive maps (equipped with the BW-topology which is metrizable). This implies that even when only a part of the spectrum of the Dirac operator is available together with a certain truncation of the

C^{⁎}

-algebra, information about the geometry can be extracted.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity