保不定半正交性的可加映射  

ADDITIVE MAPS PRESERVING INDEFINITE SEMI-ORTHOGONALITY

作　　者：赵连阔[1] 侯晋川[2] 

机构地区：[1]山西师范大学数学与计算机科学学院,临汾041004 [2]太原理工大学数学系,太原030024

出　　处：《系统科学与数学》2007年第5期697-702,共6页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金;山西省自然科学基金资助课题.

摘　　要：设H_i是实或复数域上无限维完备的不定度规空间,A_i是B(H_i)中由单位元I和一个理想生成的子代数,其中B(H_i)表示H_i上所有有界线性算子构成的代数,i=1,2.本文刻画了从A_1到A_2上双边保不定半正交性的可加满射Φ,即对任意T,S∈A_1,T^+S= 0■Φ(T)^+Φ(S)=0.主要结果表明,这样的Φ具有形式Φ(T)=UTV对任意的T∈A_1成立,这里U,V是有界线性或共轭线性可逆算子且U^+U=cI,c是非零实数.Let H be a complete indefinite inner product space of infinite dimension over real or complex field. A characterization of indefinite semi-orthogonality preserving additive surjection in both directions on unital t-subalgebras of B（H） which contains all finite rank operators is obtained. We show that such maps have the form φ（T） = UTV,arbitary T, where U and V are invertible linear or conjugate linear bounded operators with UU^＊ = cI for some nonzero real constant c. As a corollary, semi-orthogonality preserving additive surjections in both directions on unital ＊-subalgebra which contains all finite rank operators over Hilbert space are classified.

关 键 词：不定度规空间 理想 不定半正交性 

分 类 号：O177.1[理学—数学]