A characterization of -automorphism on .(H)

Authors
An, Run Ling Hou, Jin Chuan
Citation
An, Run Ling et Hou, Jin Chuan, A characterization of -automorphism on .(H), Acta mathematica Sinica. English series (Print) , 26(2), 2010, pp. 287-294
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
26
Issue
2
Year of publication
2010
Pages
287 - 294
Database
ACNP
SICI code
Abstract
Let H be a Hilbert space and A be a standard *-subalgebra of .(H). We show that a bijective map .: A.A preserves the Lie-skew product AB . BA* if and only if there is a unitary or conjugate unitary operator U . .(H) such that .(A) = UAU* for all A . A, that is, . is a linear *-isomorphism or a conjugate linear *-isomorphism.