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标准算子代数上保因子的可加映射

Additive maps on standard operator algebras preserving divisors
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摘要 设A和B分别是复Banach空间X和Y上的标准算子代数。刻画了从A到B的双边保左(右)因子或双边保因子的可加满射。 Let A and B be standard operator algebras on complex Banach spaces x and y, respectively. A characterization of additive surjection Ф： A→B which preserves left（right） divisors in both directions or preserves divisors in both directions is given.
作者 孟娇 吉国兴
机构地区 陕西师范大学数学与信息科学学院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2015年第8期20-23,33,共5页 Journal of Shandong University(Natural Science)
基金 国家自然科学基金资助项目(11371233)
关键词 标准算子代数 因子 可加映射 standard operator algebras divisors additive maps
分类号 O177.1 [理学—基础数学]
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参考文献7

  • 1LI Chi-Kwong, TSING Nam-Kiu. Linear preserver problems: A brief introduction and some special techniques[J]. Linear Algebra and its Applications, 1992, 162-164:217-235.
  • 2HOU Jinchuan, CUI Jianlian. Additive maps on standard operator algebras preserving invertibilities or zero divisors[J]. Linear Algebra and its Applications, 2003, 359(1-3):219-233.
  • 3MOLNáR L. On isomorphisms of standard operator algebras[J]. Studia Mathematica, 2000, 142(3):295-302.
  • 4OMLADI? M, ?EMRL P. Additive mappings preserving operators of rank one[J]. Linear Algebra and its Applications, 1993, 182:239-256.
  • 5LIU Lei, JI Guoxing. Maps preserving product X*Y+YX* on factor von Neumann algebras[J]. Linear and Multilinear Algebra, 2011, 59(9):951-955.
  • 6JI Guoxing, GAO Yaling. Maps preserving operator pairs whose products are projections[J]. Linear Algebra and its Applications, 2010, 433(7):1348-1364.
  • 7李荣,吉国兴.保持算子值域或核包含关系的可加映射[J].山东大学学报（理学版）,2014,49(2):42-45. 被引量：1

二级参考文献5

  • 1OUDGHIRI. M. Linear mappings preserving the kernel or the range of operators [ J]. Extracta Mathematicae, 2009, 3:251-258.
  • 2ELHODAIBI. M. On additive maps preserving the hyper-range or hyper-kernel of operators [ J ]. International Mathematical Forum, 2012, 25 : 1223-1231.
  • 3BENDAOUD M, SARIH M. Additive mappings preserving the ascent and descent of operators[ J]. Linear Algebra and its Ap- plications, 2009, 431 : 1740-1744.
  • 4DOUGLAS R G. On majorization, factorization, and range inclusion of operators on Hilbert space [ J ]. Proceedings of the American Mathematical Society, 1966, 17:413415.
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山东大学学报（理学版）
2015年 第8期

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