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

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

1997-05-30

arxiv.org/abs/math/9705211v1

Mathematics

Functional Analysis

Scientific paper

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.

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