Unitary orbits of self-adjoint operators in simple Z-stable C*-algebras

2015/02/18 by Bhishan Jacelon, Jacelon, Bhishan, Karen R. Strung +3 · 3 citations
Mathematics · Physics and Astronomy · #46L05 #46L35 #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Quantum optics and atomic interactions #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1502.05272

openalex publication_date 2015/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that in a simple, unital, exact, Z-stable C*-algebra of stable rank one, the distance between the unitary orbits of self-adjoint elements with connected spectrum is completely determined by spectral data. This fails without the assumption of Z-stability.

Citations

• The kernel of the determinant map on pure C*-algebras
• Remarks on Z-stable projectionless C*-algebras

Cited by

• Tracially lyriform C^*-algebras
• Kaplansky's problem and unitary orbits in matrix amplifications
• Self-adjoint operators in Z-stable C^*-algebras with prescribed spectral data

Related

• Self-adjoint operators in Z-stable C^*-algebras with prescribed spectral data
• Distance between unitary orbits of normal elements in simple C*-algebras of real rank zero
• Kaplansky's problem and unitary orbits in matrix amplifications
• Exponential rank and exponential length for Z-stable simple C*-algebras
• Ranks of operators in simple C*-algebras with stable rank one