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摘 要：为了研究因子von Neumann代数上完全保*-Jordan零积的满射的刻画问题，依据双边完全保*-Jordan零积和双边2-保*-Jordan零积的定义，采用完全保持的方法，证明了如果Φ是von Neumann代数A到B的一个满射，则Φ是线性或共轭线性*-同构的非零常数倍。
关键词：双边完全保*-Jordan零积;双边2-保*-Jordan零积;因子 von Neumann 代数
DOI：10.15938/j.jhust.2018.06.027
中图分类号： O152.2
文献标志码： A
文章编号： 1007-2683（2018）06-0151-04
Abstract：In order to characterize the maps completely preserving *-Jordan zero-products on factor von Neumann algebras according to the definition of bilateral complete preserving *-Jordan zero-products and bilateral 2-preserving *-Jordan zero-products taking a completely preserve approach it is proved that if Φ is a surjection of von Neumann algebra A to B，then Φis the non-zero scalar multiple of linear or conjugate linear*-isomorphism.
Keywords：bilateral complete preserving *-Jordan zero-products; bilateral 2-preserving *-Jordan zero-products; factor von Neumann algebras
参 考 文 献：
[1] CUI J. L LI C. K. Maps Preserving Product XY-YX* on Factor von Neumann Algebra[J]. Linear Algebra and Its Applications 2009 431：833-842.
[2] BAI Z. F DU S. P. Maps Preserving Products XY-YX* on von Neumann Algebras [J]. Journal of Mathematical Analysis and Applications 2012 386（1）：103-109.
[3] LIU L GUO X. Maps Preserving Product X*Y+YX* on Factor von Neumann Algebra [J]. Linear and Multilinear Algebra 2011 59：951-955.
[4] LI C. J LU F. Y FANG X. Nonlinear Mappings Preserving Product XY-YX* on Factor von Neumann Algebra[J]. Linear Algebra and Its Applications 2013 438：2339-2345.
[5] 焦美艳. Von Neumann代数套子代数上保因子交换性的线性映射[J]. 数学学报，2014，57（2）：409-416.
[6] CUI J. L PARK C. Strong Lie Skew-products Preserving Maps on Factor Von Neumann Algebra[J]. Acta Math. Sci 2012，32B（2）： 531-538.
[7] QI X. F HOU J. C. Strong Skew Commutativity Preserving Maps on Von Neumann Algebras[J]. J. Math. Anal. Appl 2013 397： 362-370.
[8] 齐霄霏，侯晋川. 保持斜 Lie 零积的可加映射[J]. 中国科学杂志社，2015，45（2）：151-165.
[9] CHEN C LU F. Y. Nonlinear Maps Preserving Higher Dimensional Numerical Range of Skew Lie Product of Operators [J]. Operator and Matrices 2016 10（2）：335-344.
[10]HOU J. C HUANG L. Characterizing Isomorphisms in Terms of Completely Preserving Invertibility or Spectrum [J]. Journal of Mathematical Analysis and Applications 2009 359（1）： 81-87.
[11]黄丽，路召飞，李俊林. 标准算子代数上完全保斜幂等性的可加映射[J]. 中北大学学报： 自然科学版，2011，32（1）：71-73.
[12]HUANG L LIU Y. X. Maps Completely Preserving Commutativity and Maps Completely Preserving Jordan Zero-product[J]. Linear Algebra and Its Applications 2014 462（12）：233-249.
[13]刘艳晓，黄丽. 完全保持不同因子交換性的映射[J]. 太原科技大学学报，2015，36（3）：237-240.
[14]李文慧. 完全保持斜Jordan零积和斜交换性映射的研究[D]. 太原：太原科技大学，2017.
（编辑：温泽宇）
关键词：双边完全保*-Jordan零积;双边2-保*-Jordan零积;因子 von Neumann 代数
DOI：10.15938/j.jhust.2018.06.027
中图分类号： O152.2
文献标志码： A
文章编号： 1007-2683（2018）06-0151-04
Abstract：In order to characterize the maps completely preserving *-Jordan zero-products on factor von Neumann algebras according to the definition of bilateral complete preserving *-Jordan zero-products and bilateral 2-preserving *-Jordan zero-products taking a completely preserve approach it is proved that if Φ is a surjection of von Neumann algebra A to B，then Φis the non-zero scalar multiple of linear or conjugate linear*-isomorphism.
Keywords：bilateral complete preserving *-Jordan zero-products; bilateral 2-preserving *-Jordan zero-products; factor von Neumann algebras
参 考 文 献：
[1] CUI J. L LI C. K. Maps Preserving Product XY-YX* on Factor von Neumann Algebra[J]. Linear Algebra and Its Applications 2009 431：833-842.
[2] BAI Z. F DU S. P. Maps Preserving Products XY-YX* on von Neumann Algebras [J]. Journal of Mathematical Analysis and Applications 2012 386（1）：103-109.
[3] LIU L GUO X. Maps Preserving Product X*Y+YX* on Factor von Neumann Algebra [J]. Linear and Multilinear Algebra 2011 59：951-955.
[4] LI C. J LU F. Y FANG X. Nonlinear Mappings Preserving Product XY-YX* on Factor von Neumann Algebra[J]. Linear Algebra and Its Applications 2013 438：2339-2345.
[5] 焦美艳. Von Neumann代数套子代数上保因子交换性的线性映射[J]. 数学学报，2014，57（2）：409-416.
[6] CUI J. L PARK C. Strong Lie Skew-products Preserving Maps on Factor Von Neumann Algebra[J]. Acta Math. Sci 2012，32B（2）： 531-538.
[7] QI X. F HOU J. C. Strong Skew Commutativity Preserving Maps on Von Neumann Algebras[J]. J. Math. Anal. Appl 2013 397： 362-370.
[8] 齐霄霏，侯晋川. 保持斜 Lie 零积的可加映射[J]. 中国科学杂志社，2015，45（2）：151-165.
[9] CHEN C LU F. Y. Nonlinear Maps Preserving Higher Dimensional Numerical Range of Skew Lie Product of Operators [J]. Operator and Matrices 2016 10（2）：335-344.
[10]HOU J. C HUANG L. Characterizing Isomorphisms in Terms of Completely Preserving Invertibility or Spectrum [J]. Journal of Mathematical Analysis and Applications 2009 359（1）： 81-87.
[11]黄丽，路召飞，李俊林. 标准算子代数上完全保斜幂等性的可加映射[J]. 中北大学学报： 自然科学版，2011，32（1）：71-73.
[12]HUANG L LIU Y. X. Maps Completely Preserving Commutativity and Maps Completely Preserving Jordan Zero-product[J]. Linear Algebra and Its Applications 2014 462（12）：233-249.
[13]刘艳晓，黄丽. 完全保持不同因子交換性的映射[J]. 太原科技大学学报，2015，36（3）：237-240.
[14]李文慧. 完全保持斜Jordan零积和斜交换性映射的研究[D]. 太原：太原科技大学，2017.
（编辑：温泽宇）