Transformations of the unitary group on a Hilbert space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Molnar, Lajos²  Semrl, Peter¹ 

[1] Univ Ljubljana, Fac Math & Phys, SI-1000 Ljubljana, Slovenia

[2] Univ Debrecen, Inst Math, H-4010 Debrecen, Hungary

关键词: Hilbert space;    Unitary group;    Automorphisms;    Commutativity preserving maps;   

DOI  :  10.1016/j.jmaa.2011.11.007

来源: Elsevier

【 摘 要 】

Let H be an infinite dimensional separable complex Hilbert space and U be the group of all unitary operators on H. Motivated by the algebraic properties of surjective isometrics of U that have recently been revealed, and also by some classical results related to automorphisms of the unitary groups of operator algebras, we determine the structures of bijective transformations of U that respect certain algebraic operations. These are, among others, the usual product of operators, the Jordan triple product, the inverted Jordan triple product, and the multiplicative commutator. Our basic approach to obtain these results is. the use of commutativity preserving transformations on the unitary group. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free