完全保持斜Lie零积的映射Maps of Completely Preserving Skew Lie Zero Products
李文慧,黄丽,张瑜
摘要(Abstract)：
对Hilbert空间上的投影算子上双边保正交性的双射的刻画,得到了复无限维Hilbert空间上的~*-标准算子代数之间完全保持斜Lie零积的满射的具体结构形式,进而证明了这样的映射是同构或者共轭同构的常数倍。
关键词(KeyWords)： *-标准算子代数;完全保持;斜Lie零积
基金项目(Foundation): 国家自然科学基金青年基金项目(11501401)
作者(Author): 李文慧,黄丽,张瑜
参考文献(References)：
- [1]MOLNAR L.A condition for a subspace of B(H)to be an ideal[J].Linear Algebra and its Applications,1996,235:229-234.
- [2]CHEBOTAR M,GTFONG.On maps preserving zeros ofthe polynomial[J].Linear Algebra and its Applications,2005,408:230-243.
- [3]CUI J,LI C.Maps preserving product XY-YX*on factor von Neumann algebras[J].Linear Algebra and its Applications,2009,431(5):833-842.
- [4]BAI Z,DU S.Maps preserving products XY-YX*on von Neumann algebras[J].Journal of Mathematical Analysis and Applications,2012,386(1):103-109.
- [5]齐霄霏,侯晋川,崔建莲.保持斜ξ-Lie零积的可加映射[J].中国科学:数学,2015,45(2):151-165.
- [6]HOU J,HUANG L.Maps completely preserving idempotents and maps completely preserving square-zero operators[J].Israel Journal of Mathematics,2010,176(1):363-380.
- [7]HOU J,HUANG L.Characterizing isomorphisms in terms of completely preserving invertibility or spectrum[J].Journal of Mathematical Analysis and Applications,2009,359(1):81-87.
- [8]HUANG L,LIU Y.Maps completely preserving commutativity and maps completely preserving Jordan zero-product[J].Linear Algebra and Its Applications,2014,462(12):233-249.
- [9]刘艳晓,黄丽.完全保持不同因子交换性的映射[J].太原科技大学学报,2015,36(3):237-240.
- [10]黄丽,侯晋川.标准算子代数上完全保可逆性或零因子的映射[J].山西大学学报:自然科学版,2009,32(1):5-8.
- [11]UHLHORN U.Representation of symmetry transformations in quantum mechanics[J].Arkiv Fysik,1963,23:307-340.