Algebraic reflexivity of isometry groups and automorphism groups of some operator structures

作者：Botelho Fernanda; Jamison James; Molnar Lajos^*

来源：Journal of Mathematical Analysis and Applications, 2013, 408(1): 177-195.

DOI：10.1016/j.jmaa.2013.06.001

• Hilbert space operators
• Operator structures
• Surjective isornetries
• Automorphisms
• Algebraic reflexivity of transformation groups

We establish the algebraic reflexivity of three isometry groups of operator structures: the group of all surjective isometries on the unitary group, the group of all surjective isometries on the set of all positive invertible operators equipped with the Thompson metric, and the group of all surjective isometries on the general linear group of B(H), the operator algebra over a complex infinite dimensional separable Hilbert space H. We show that those isometry groups coincide with certain groups of automorphisms of corresponding structures and hence we also obtain the reflexivity of some automorphism groups.

• 出版日期2013-12-1