Banach Gelfand三元组与通过等价双模的核定理
Banach Gelfand Triples with Kernel Theorems via Equivalence Bimodules
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中文总结 AI 辅助
本文通过等价双模构造Banach Gelfand三元组，证明有限生成投影Hilbert C*-模的核定理，并应用于Heisenberg模，得到时频分析的新核定理。
中文摘要 AI 辅助
系数C*-代数配备有限忠实迹的Hilbert C*-模生成Banach Gelfand三元组。这为Hilbert C*-模的函数空间解释提供了自然框架。特别地，当模是有限生成且投影的，其外部张量积与投影张量积良好交互，使我们能够推导出Hilbert C*-模的抽象核定理。作为应用，我们将结果应用于Heisenberg模，并获得时频分析的新核定理。
英文摘要
Hilbert C*-modules whose coefficient C*-algebra is equipped with a finite faithful trace generate Banach Gelfand triples. This provides a natural setting for a function space interpretation of Hilbert C*-modules. In particular, when the modules are finitely generated and projective, their external tensor products interact well with projective tensor products, allowing us to derive abstract kernel theorems for Hilbert C*-modules. As an application, we apply our results to Heisenberg modules and obtain new kernel theorems for time-frequency analysis.
