三角代数上Jordan高阶导子的刻画
Characterization of Jordan Higher Derivations on Triangular Algebras
设U=Tri(A,M,B)是含单位元I的三角代数,φ={φn}n∈N是U上一簇线性映射.本文证明了:如果对任意U,V∈U且UV=VU=I,有φn(UV+VU)=∑i+j=n(φi(U)φj(V)+φi(V)φj(U)),则φ={φn}n∈N是U上高阶导子.作为应用,得到了套代数上Jordan高阶导子的一个刻画.
Let U=Tri(A, M, B) be the triangular algebra with identity I, and let φ={φn}n∈N be a family of linear maps on U. We show that if φ={φn}n∈N satisfying φn(UV+VU)=∑i+j=n(φi(U)φj(V)+φi(V)φj(U)) whenever U, V∈U with UV=VU=I, then it is a higher derivation. As its application, we give a different characterization of Jordan higher derivations on nest algebras.
三角代数 / Jordan高阶导子 / 高阶导子 {{custom_keyword}} /
Triangular algebra / Jordan higher derivation / higher derivation {{custom_keyword}} /
[1] An R., Hou J., Characterizations of derivations on triangular rings: Additive maps derivable at idempotents, Linear Algebra Appl., 2009, 431: 1070-1080.
[2] Brešar M., Characterizing homomorphisms, multipliers and derivations in rings with idempotents, Proc. Roy. Soc. Edinburgh Sect., 2007, 137: 9-21.
[3] Hou J., Qi X., Additive maps derivable at some points on J-subspace lattice algebras, Linear Algebra Appl., 2008, 429: 1851-1863.
[4] Jing W., On Jordan all-derivable points of B(H), Linear Algebra Appl., 2009, 430: 941-946.
[5] Li J., Guo J., Characterizations of higher derivations and Jordan higher derivations on CSL algebras, Bull. Aust. Math. Soc., 2011, 83: 486-499.
[6] Lu F., Characterizations of derivations and Jordan derivations on Banach algebras, Linear Algebra Appl., 2009, 430: 2233-2239.
[7] Wei F., Xiao Z., Higher derivations of triangular algebras and its generalizations, Linear Algebra Appl., 2011, 435: 1034-1054.
[8] Zeng H., Zhu J., Jordan higher all-derivable points on nontrivial nest algebras, Linear Algebra Appl., 2011, 434: 463-474.
[9] Zhang X., An R., Hou J., Characterizations of higher derivations on CSL algebras, Epo. Math., 2013, 31: 392-404.
[10] Zhao J., Zhu J., Jordan higher all-derivable points in triangular algebras, Linear Algebra Appl., 2012, 436: 3072-3086.
[11] Zhao S., Zhu J., Jordan all-derivable points in the algebra of all upper triangular matrices, Linear Algebra Appl., 2010, 433: 1922-1938.
[12] Zhu J., All-derivable points of operator algebras, Linear Algebra Appl., 2006, 419: 251-255.
[13] Zhu J., Xiong X., Derivable mappings at unit operator on nest algebras, Linear Algebra Appl., 2007, 422: 721-735.
国家自然科学基金资助项目(11471199);陕西师范大学研究生培养创新基金(2015CXB007)
/
〈 | 〉 |