Jorgense不等式在范数代数中的推广(英文)

A Generalization of Jorgense's Inequality in Normed Algebras

证明了一个范数代数中的JORGENSEN类不等式 :设R是范数代数 ,〈a ,b〉 R是离散非ANILPO TENT群 ,那么 ,可以得到 (1)‖ a‖ +｜ (a ,b) -a2 ｜≥｜a｜2 和 (2 )‖ a‖ +｜b -a2 ｜≥｜a｜2 .特别有 :max(｜a｜2｜ (a ,b) -a2 ｜ ,｜a - 1｜)≥ 2 - 3,max(｜a｜2 ｜b-a2 ｜ ,｜a - 1｜)≥ 2 - 3.

In this paper we give a generalization of Jorgensen's inequality in normed algebras: Let R be a normed algebra.Assume that 〈a,b〉R is a discrete non-a-nilpotent group.Then the following conditions hold (1) ‖‖+｜(a,b)-a 2｜≥ ｜a｜ 2,(2) ‖‖+｜b-a 2｜≥ ｜a｜ 2.In particular, max(｜a｜ -2 ｜(a,b)-a 2｜, ｜a-1｜)≥ 2-3,max(｜a｜ -2 ｜b-a 2｜,｜a-1｜)≥ 2-3. MR