2024/03/09 by Ved Prakash Gupta, Sumit Kumar, Gupta, Ved Prakash +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2403.05967
openalex publication_date 2024/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given any irreducible inclusion \mB ⊂ \mA of unital C^*-algebras with a finite-index conditional expectation E: \mA → \mB, we show that the set of E-compatible intermediate C^*-subalgebras is finite, thereby generalizing a finiteness result of Ino and Watatani (from \citeIW). A finiteness result for a certain collection of intermediate C^*-subalgebras of a non-irreducible inclusion of simple unital C^*-algebras is also obtained, which provides a C^*-version of a finiteness result of Khoshkam and Mashood (from \citeKM). Apart from these finiteness results, comparisons between various notions of distance between subalgebras of operator algebras by Kadison-Kastler, Christensen and Mashood-Taylor are made. Further, these comparisons are used satisfactorily to provide some concrete calculations of distance between operator algebras associated to two distinct subgroups of a given discrete group.