期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 506, 期 1, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2021.125563
关键词
Contractive projection; von Neumann inequality; C*-algebra; JB*-algebra
资金
- Junta de Andalucia grant [FQM199]
By studying projections of complete normed complex algebras under different conditions, a series of results about the properties of the algebras and satisfying inequalities have been obtained.
Let A be a complete normed complex algebra, let 7r : A-+ A be a nonzero contractive linear projection, and consider 7r(A) as a complete normed complex algebra under the product (x, y)-+ 7r(xy). We prove the following results. -If A is unital and associative (respectively, alternative) and satisfies the von Neumann inequality, and if 7r satisfies the weak conditional expectation property (WCE) 7r(7r(a)7r(b)) = 7r(7r(a)b) = 7r(a7r(b)) for all a, b is an element of A, then 7r(A) is unital and associative (respectively, alternative) and satisfies the von Neumann inequality. -If A is an Arazy algebra, and if 7r satisfies the weak Jordan conditional expectation (namely the symmetrization of (WCE)), then 7r(A) is an Arazy algebra. (We note that, in the possibly non power-associative setting, Arazy algebras are the adequate substitutes of complete normed unital power-associative complex algebras satisfying the von Neumann inequality.) -If the closed multiplication algebra of A satisfies the von Neumann inequality, and if 7r is an elementary operator, then the closed multiplication algebra of 7r(A) satisfies the von Neumann inequality. (c) 2021 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据