Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C*-algebras

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Hatori, Osamu¹  Molnar, Lajos² 

[1] Niigata Univ, Dept Math, Fac Sci, Niigata 9502181, Japan

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

关键词: Isometry;    Jordan *-isomorphism;    Unitary group;    Positive element;    Thompson metric;    C*-algebra;    von Neumann algebra;    Function algebra;   

DOI  :  10.1016/j.jmaa.2013.06.065

来源: Elsevier

【 摘 要 】

We show that the existence of a surjective isometry (which is merely a distance preserving map) between the unitary groups of unital C*-algebras implies the existence of a Jordan *-isomorphism between the algebras. In the case of von Neumann algebras we describe the structure of those isometries showing that any of them is extendible to a real linear Jordan *-isomorphism between the underlying algebras multiplied by a fixed unitary element. We present a result of similar spirit for the surjective Thompson isometries between the spaces of all invertible positive elements in unital C*-algebras. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free