发表机构
School of Mathematics, Jilin University（吉林大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对具有有界近似单位元且Morita等价的Banach代数，研究其闭双边理想的诱导对应关系，证明几何理想在Morita诱导下保持不变，并将结果应用于ℓ^p一致Roe代数与ℓ^p一致代数的Morita等价研究。
AI 中文摘要
给定两个具有有界近似单位元且按Paravicini意义下Morita等价的Banach代数，我们描述它们的闭双边理想之间的诱导对应关系，刻画对应理想何时为Morita等价，并证明对应的商代数总是Morita等价的。我们还证明由相容稠密代数核定义的几何理想在Morita诱导下保持不变，并给出用于识别对应理想的局部化子模判据。我们将这些结果应用于有界几何度量空间X的ℓ^p一致Roe代数B_u^p(X)与ℓ^p一致代数UB^p(X)之间的Morita等价研究。作为一个技术组成部分，我们证明UB^p(X)具有由投影构成的有界近似单位元。Morita诱导进而确定了两个代数的几何理想格，因此UB^p(X)的几何理想对应于X的有界粗结构的理想。
英文摘要
Given Banach algebras with bounded approximate identities that are Morita equivalent in the sense of Paravicini, we give explicit formulas for the induced correspondence between their closed two-sided ideals, characterize when corresponding ideals are Morita equivalent through the restricted bimodules, and show that corresponding quotients are Morita equivalent. We then isolate two mechanisms for preserving distinguished classes of ideals: compatible dense algebraic cores and localized Morita submodules. The latter shows that, for equivalent locally compact Hausdorff étale groupoids with paracompact unit spaces, the associated Morita equivalence of reduced groupoid $L^p$-operator algebras preserves dynamical ideals. The former applies to the Morita equivalence between the $\ell^p$ uniform Roe algebra and the $\ell^p$ uniform algebra of a bounded geometry metric space, identifying their geometric ideals. As a technical ingredient, we prove that the $\ell^p$ uniform algebra has a bounded approximate identity of projections.
Comments24 pages. This paper corrects, expands, and supersedes the material on Morita equivalence and geometric ideals in Section 7 of arXiv:2606.11586v1. Compared with version 1, a section applying our results to dynamical ideals in reduced groupoid $L^p$-operator algebras has been added
