Norms of elementary operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Norms of elementary operators

Authors:	Hong-Ke Du Yue-Qing Wang Gui-Bao Gao

Institution:	College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, People's Republic of China ; College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, People's Republic of China ; College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, People's Republic of China

Abstract:	Let and , $1\leq i\leq n$ , be bounded linear operators acting on a separable Hilbert space $\mathcal H$ . In this note, we prove that $\sup\{\parallel\sum_{i=1}^n A_iXB_i\parallel~: X\in \mathcal{B(H)}, \parallelX... ...{\parallel\sum_{i=1}^n A_iUB_i\parallel : UU^=U^U=I, U\in {\mathcal{B(H)}}\}.$ Moreover, we prove that there exists an operator with $\parallel X_0\parallel =1$ such that $\parallel\sum_{i=1}^n A_iX_0B_i\parallel =\sup\{\parallel\sum_{i=1}^n A_iXB_i\parallel : X\in {\mathcal{B(H)}}, \parallelX\parallel \leq 1\}$ if and only if there exists a unitary $U_0\in \mathcal{B(H)}$ such that $\parallel\sum_{i=1}^n A_iU_0B_i\parallel =$ $\sup\{\parallel\sum_{i=1}^n A_iXB_i\parallel : X\in {\mathcal{B(H)}}, \parallelX\parallel \leq 1\}.$

Keywords:	Elementary operator norm-attainability unitary

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文