保持二次算子的可加映射Additive maps preserving quadratic operators
孟红叶;吉国兴;
摘要(Abstract)：
设X是具有无限重复度的无限维或维数不小于3的有限维复Banach空间,B(X)是X上全体有界线性算子组成的Banach代数.首先证明了单位算子不能表示成3个平方幂零算子之和,利用算子分块矩阵技巧获得了平方幂零算子的本质特征.以此特征为基础,刻画了B(X)上双边保持二次算子可加满射的结构.
关键词(KeyWords)： 二次算子;幂等算子;平方幂零算子;可加映射
基金项目(Foundation): 国家自然科学基金(11371233)
作者(Authors): 孟红叶;吉国兴;
参考文献(References)：
- [1]Bai Zhaofang,Hou Jinchuan.Linear maps and additive maps that preserve operators annihilated by a polynomoal[J].Math.Anal.Appl.,2002,271:139-154.
- [2]Bai Zhaofang,Hou Jinchuan.Additive maps preserving nilpotent operators or spectral radius[J].Acta.Math.Sin,(Engl.Ser.),2005,21:1167-1182.
- [3]Cao Chongguang,Zhang Xian.Additive operators preserving idempotent matrices over fields and applications[J].Linear Algebra Appl.,1996,248:327-338.
- [4]Hadwin L B.Local multiplications on algebras spanned by idempotents[J].Linear and Multilinear Algebra,1994,37:259-263.
- [5]侯晋川,崔建莲.算子代数上线性映射引论[M].北京:科学出版社,2002.
- [6]Kuzma B.Additive idempotence preservers[J].Linear Algebra Appl.,2002,335:103-117.
- [7]Omladic M,Semrl P.Additive mappings preserving operators of rank one[J].Linear Algebra Appl.,1993,182:239-256.
- [8]Oudghiri M,Souilah K.Linear preservers of quadratic operators[J].Mediterranean Journal of Mthematics,2016,13:4929-4938.
- [9]Semrl P.Linear mappings preserving square-zero matrics[J].Bull.Australian Math.Soc.,1993,48:365-370.
- [10]Jin-hsien W,Wu Peiyuan.Sums of square-zero opeators[J].Studia Mathematica,1991,99:115-127.
- [11]Wu Jing,Li Pengtong,Lu Shijie.Additive mappings that preserve rank one nilpotent operators[J].Linear Algebra Appl.,2003,367:213-224.
- [12]Wu Peiyuan.Additive combimations of special operators[J].Functional Analysis and Operator Theory,1994,30:337-361.