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《Journal of Baoji University of Arts and Sciences(Natural Science Edition)》 2009-01
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A class of bijective maps preserving *-multiplicativity on B(H)

QU Fan-lian(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)  
Aim It is described that the concrete form for a class of bijective maps φ preserving *-multiplicativity on the algebras B(H) of all bounded linear operators, acting on a complex Hilbert space H with dim H≥2. Methods The bijectivity of φ and *-multiplicativity-preserving property of φ are used to prove the main theorem. Results It is proved that a bijective map φ preservers *-multiplicativity if and only if φ is a *-isomorphism or a conjugate *-isomorphism. Related results for bijective maps preserving *-anti-multiplicativity are also obtained. Conclusion The property of maps preserving *-multiplicativity is considered as a characteristic invariant of B(H), providing the information of classification of operator algebras from a new view.
【CateGory Index】: O177.1
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【Co-citations】
Chinese Journal Full-text Database 10 Hits
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3 LI Hong-xia~1 DUAN Ying-tao~2 1.School of Sciences,Southwest University of Science and Technology,Mianyang,China 621010,2.Department of Mathmathics,Leshan Teachers College,Lesha,614000,Sichuan;Derivable Mappings at Zero Point on Standard Operator Algebras[J];Journal of Neijiang Normal University;2008-10
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5 LI Song-xiao(Department of Mathematics, JiaYing University,Meizhou,Guangdong,514015,China);Spectrum-Preserving Linear Maps on C~*-algebra of Reak Rabj Zeri[J];Journal of Shanxi Teachers University(Natural Science Edition);2004-01
6 HUANG Li1,2,HOU Jin-chuan3(1.School of Mathematical Science,Shanxi University,Taiyuan 030006,China;2.Shool of Applied Science Taiyuan Unversity of Science and Technology,Taiyuan 030024,China;3.Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China);Maps Completely Preserving Invertibility or Zero Divisors on Standard Operator Algebras[J];Journal of Shanxi University(Natural Science Edition);2009-01
7 HUANG Li~* HOU Jinchuan~(**) ~*Department of Mathematics,Shanxi University,Taiyuan 030006,China. ~(**)Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China.;Maps Preserving Spectral Functions of Operator Products[J];Chinese Annals of Mathematics;2007-06
8 ZHANG Fang-juan,JI Guo-xing(College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,Shaanxi,China);Additive maps preserving orthogonality on B(H)[J];Journal of Shaanxi Normal University(Natural Science Edition);2005-04
9 HOU Jin-chuan1,2,HE Kan1(1.School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China;2.Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China);Distance Preseving Maps and Completely Distance Preseving Maps on the Schatten-p Class[J];Journal of Shanxi University(Natural Science Edition);2009-04
10 YU Bao-min, XUE She-jiao(Department of Mathematics and Information Science, Weinan Teachers University, Weinan 714000, China);A Note on Several Topologies in Operator Spaces of Hilbert Space[J];Journal of Weinan Teachers University;2009-02
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