On topological reflexivity of the groups of *-automorphisms and surjective isometries of (H)

摘要

Let X be a Banach space. Denote by (X) the algebra of all bounded linear operators acting on X. A subset (X) is called algebraically, respectively topologically, reflexive if the implications. respectively hold ture. In this case one can say that is completely determined by its local or approximately local actions. This concept of reflexivity proved very useful in the analysis of operator algebras (see[7] and the references therein). If X is an operator algebra acting on a Hilbert space, then probably the most important sets of linear transformations on X are the derivation algebra, the automorphism group, and the isometry group.