Multiplicative *-Lie isomorphisms between von Neumann algebras

被引：6

作者：

Bai, Zhaofang ^{[1
]}

Du, Shuanping ^{[1
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2012年 / 60卷 / 03期

基金：

中国国家自然科学基金;

关键词：

*-Lie isomorphism; von Neumann algebra; PRIME-RINGS; INVOLUTION;

D O I：

10.1080/03081087.2011.592142

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M, N be von Neumann algebras with no central summands of type I-1 or I-2. If Phi : M -> N is a multiplicative *-Lie isomorphism, then there is a central projection E is an element of N such that modulo a centre-valued map which annihilates commutators, E Phi is a linear Lie *-homomorphism and (I - E)Phi is a conjugate linear Lie *-homomorphism.

引用

页码：311 / 322

页数：12

共 10 条

[1] Multiplicative *-Lie isomorphisms between factors [J].

Bai, Zhaofang ;

Du, Shuanping .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 346 (01) :327-335

[2] LIE ISOMORPHISMS IN PRIME-RINGS WITH INVOLUTION [J].

BEIDAR, KI ;

MARTINDALE, WS ;

MIKHALEV, AV .

JOURNAL OF ALGEBRA, 1994, 169 (01) :304-327

[3] On Herstein's Lie map conjectures, I [J].

Beidar, KI ;

Bresar, M ;

Chebotar, MA ;

Martindale, WS .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (10) :4235-4260

[4] Lie isomorphisms of non-GPI rings with involution [J].

Blau, PS .

COMMUNICATIONS IN ALGEBRA, 1999, 27 (05) :2345-2373

[5] CENTRALIZING MAPPINGS ON VONNEUMANN-ALGEBRAS [J].

BRESAR, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 111 (02) :501-510

[6] On Lie isomorphisms in prime rings with involution [J].

Chebotar, MA .

COMMUNICATIONS IN ALGEBRA, 1999, 27 (06) :2767-2777

[7]

Kadison R. V., 1983, Fundamentals of the Theory of Operator Algebras I

[8]

Kadison RV, 1986, FUNDAMENTALS THEORY, VII

[9] LIE ISOMORPHISMS OF PRIME RINGS [J].

MARTINDALE, WS .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 142 (AUG) :437-+

[10] LIE HOMOMORPHISMS OF OPERATOR ALGEBRAS [J].

MIERS, CR .

PACIFIC JOURNAL OF MATHEMATICS, 1971, 38 (03) :717-&

← 1 →