2005/11/14 by Bebe Prunaru, Prunaru, Bebe · 1 citation
Mathematics · #46L07 #47B35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Primary 47L80 #Secondary 47B20 #math.FA #math.OA #msc:46L07 #msc:47B20 #msc:47B35 #msc:47L80
paper · pdf · doi:10.48550/arxiv.math/0511340
arxiv created 2005/11/14 · openalex publication_date 2005/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A family \Tj\j∈ J of commuting Hilbert space operators is said to be a spherical isometry if ∑j∈ JT^*jTj=1 in the weak operator topology. We show that every commuting family \Cal F of spherical isometries has a commuting normal extension \Cal F. Moreover, if \Cal F is minimal, then there exists a natural short exact sequence 0→\Cal C→ C^*(\Cal F)→ C^*(\Cal F)→ 0 with a completely isometric cross-section, where \Cal C is the commutator ideal in C^*(\Cal F). We also show that the space of Toeplitz operators associated to \Cal F is completely isometric to the commutant of the minimal normal extension \Cal F. Applications of these results are given for Toeplitz operators on strictly pseudoconvex or bounded symmetric domains.