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

Botelho, Fernanda and Jamison, James and Molnár, Lajos (2013) Algebraic reflexivity of isometry groups and automorphism groups of some operator structures. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, inpres. pp. 1-23. ISSN 0022-247X

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Abstract

We establish the algebraic re exivity 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 re exivity of some automorphism groups.

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