Reflexivity of the automorphism and isometry groups of some standard operator algebras

1997/05/30 by Lajos Molnár, Lajos Molnar, Molnar, Lajos
Mathematics · #46L40 #47B35 #47B49 #47D25 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46L40 #msc:47B35 #msc:47B49 #msc:47D25

paper · pdf · doi:10.48550/arxiv.math/9705211

arxiv created 1997/05/30 · openalex publication_date 1997/05/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give an example of a proper standard C*-algebra (a proper C*-subalgebra of B(H) containing C(H)) whose automorphism and isometry groups are topologically reflexive. Furthermore, we prove that in the case of extensions of C(H) by separable commutative C*-algebras, these groups are algebraically reflexive. Concerning the most well-known extensions of C(H) by the algebra of all continuous complex valued functions on the perimeter of the unit disc, we show that the automorphism and isometry groups are topologically nonreflexive.

Citations

• Representations, automorphisms, and derivations of some operator algebras

Related

• The automorphism and isometry groups of l_∞(N, B(H)) are topologically reflexive
• Reflexivity of the automorphism and isometry groups of the suspension of B(H)
• A reflexivity problem concerning the C^*-algebra C(X)⊗ B(H)
• Reflexivity of the isometry group of some classical spaces
• Algebraic Reflexivity of the set of n-Isometries on C(X,E)