کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4615800 | 1339329 | 2014 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Star order on JBW algebras
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The goal of the paper is to extend the star order from associative algebras to non-associative Jordan Banach structures. Let A be a JBW algebra. We define a relation on A as the set of all pairs (a,b)âAÃA such that the range projections of a and bâa are orthogonal. We show that this relation defines a partial order on A which, in the case of the self-adjoint part of a von Neumann algebra, gives the star order. After showing basic properties of this order we shall prove the following preserver theorem: Let A be a JBW algebra without Type I2 direct summand and let Ï be a continuous map from A to B preserving the star order in both directions. If for each scalar λ one has Ï(λ1)=f(λ)z, where f is a (continuous) function and z is a central invertible element, then there is a unique Jordan isomorphism Ï:AâB such that Ï(a)=Ï(f(a))z. Moreover, we show that if A is a Type In factor, where nâ 2, then the equation above holds for all continuous maps preserving the star order in both directions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 417, Issue 2, 15 September 2014, Pages 873-888
Journal: Journal of Mathematical Analysis and Applications - Volume 417, Issue 2, 15 September 2014, Pages 873-888
نویسندگان
Martin Bohata, Jan Hamhalter,