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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:408

Article

Botelho, Fernanda¹  Jamison, James¹  Molnar, Lajos² 

[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

[2] Univ Debrecen, Inst Math, MTA DE Lendulet Funct Anal Res Grp, H-4010 Debrecen, Hungary

关键词: Hilbert space operators;    Operator structures;    Surjective isornetries;    Automorphisms;    Algebraic reflexivity of transformation groups;   

DOI  :  10.1016/j.jmaa.2013.06.001

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free