Browse > Article
http://dx.doi.org/10.4134/BKMS.2013.50.6.2027

ADDITIVITY OF JORDAN TRIPLE PRODUCT HOMOMORPHISMS ON GENERALIZED MATRIX ALGEBRAS  

Kim, Sang Og (Department of Mathematics Hallym University)
Park, Choonkil (Research Institute for Natural Sciences Hanyang University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.6, 2013 , pp. 2027-2034 More about this Journal
Abstract
In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from $M_n(\mathcal{A})$ ($\mathcal{A}$ is not necessarily a prime algebra) onto an arbitrary ring $\mathcal{R}^{\prime}$ is additive.
Keywords
Jordan triple product homomorphism; generalized matrix algebra; additive map;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 X. Cheng and W. Jing, Additivity of maps on triangular algebras, Electron. J. Linear Algebra 17 (2008), 597-615.
2 I. Hakeda, Additivity of Jordan *-maps on AW*-algebras, Proc. Amer. Math. Soc. 96 (1986), no. 3, 413-420.
3 J. Hakeda and K. Saito, Additivity of Jordan *-maps between operator algebras, J. Math. Soc. Japan 38 (1986), no. 3, 403-408.   DOI
4 P. Ji, Jordan maps on triangular algebras, Linear Algebra Appl. 426 (2007), no. 1, 190-198.   DOI   ScienceOn
5 P. Ji, R. Liu, and Y. Zhao, Nonlinear Lie triple derivations of triangular algebras, Linear Multilinear Algebra 60 (2012), no. 10, 1155-1164.   DOI   ScienceOn
6 W. Jing, Additivity of Jordan elementary maps on rings, arXiv:0706.0488v1 [math.RA] 4 Jun 2007.
7 B. Kuzma, Jordan triple product homomorphisms, Monatsh. Math. 149 (2006), no. 2, 119-128.   DOI
8 P. Li and W. Jing, Jordan elementary maps on rings, Linear Algebra Appl. 382 (2004), 237-245.   DOI   ScienceOn
9 P. Li and F. Lu, Additivity of Jordan elementary maps on nest algebras, Linear Algebra Appl. 400 (2005), 327-338.   DOI   ScienceOn
10 Y. Li and Z. Xiao, Additivity of maps on generalized matrix algebras, Electron. J. Linear Algebra 22 (2011), 743-757.
11 Z. Ling and F. Lu, Jordan maps of nest algebras, Linear Algebra Appl. 387 (2004), 361-368.   DOI   ScienceOn
12 F. Lu, Jordan triple maps, Linear Algebra Appl. 375 (2003), 311-317.   DOI   ScienceOn
13 F. Lu, Jordan maps on associative algebras, Comm. Algebra 31 (2003), no. 5, 2273-2286.   DOI   ScienceOn
14 F. Lu, Multiplicative mappings of operator algebras, Linear Algebra Appl. 347 (2002), 283-291.   DOI   ScienceOn
15 F. Lu, Additivity of Jordan maps on standard operator algebras, Linear Algebra Appl. 357 (2002), 123-131.   DOI   ScienceOn
16 A. J. C. Martin and C. M. Gonzalez, The Banach-Lie group of Lie triple automorphisms of an H*-algebras, Acta Math. Sci. Ser. B Engl. Ed. 30 (2010), no. 4, 1219-1226.
17 A. J. C. Martin and C. M. Gonzalez, A linear approach to Lie triple automorphisms of H*-algebras, J. Korean Math. Soc. 48 (2011), no. 1, 117-132.   과학기술학회마을   DOI   ScienceOn
18 W. S. Martindale III, When are multiplicative mappings additive?, Proc. Amer. Math. Soc. 21 (1969), 695-698.
19 L. Molnar, On isomorphisms of standard operator algebras, Studia Math. 142 (2000), no. 3, 295-302.
20 L. Molnar and P. Semrl, Elementary operators on standard algebras, Linear Multilinear Algebra 50 (2002), no. 4, 315-319.   DOI   ScienceOn
21 P. Semrl, Isomorphisms of standard operator algebras, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1851-1885.   DOI   ScienceOn
22 Z. Xiao and F.Wei, Commuting mappings of generalized matrix algebras, Linear Algebra Appl. 433 (2010), no. 11-12, 2178-2197.   DOI   ScienceOn
23 Z. Xiao and F.Wei, Lie triple derivations of triangular algebras, Linear Algebra Appl. 437 (2012), no. 5, 1234-1249.   DOI   ScienceOn