2018/12/20 by PN Shankar, Shankar, P.
Mathematics · #46L07 #46L52 #47A13 #47L80 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1812.08574
openalex publication_date 2018/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we show that, if S∈ B(H) is irreducible and essential unitary, then \S,SS^*\ is a hyperrigid generator for the unital C^*-algebra T generated by \S,SS^*\. We prove that, if T is an operator in B(H) that generates an unital C^*-algebra A then \T,T^*T,TT^*\ is a hyperrigid generator for A. As a corollary it follows that, if T∈ B(H) is normal then \T,TT^*\ is hyperrigid generator for the unital C^*-algebra generated by T and if T∈ B(H) is unitary then \T\ is hyperrigid generator for the C^*-algebra generated by T. We show that if V∈ B(H) is an isometry (not unitary) that generates the C^*-algebra A then the minimal generating set \V\ is not hyperrigid for A.