ON COMMUTATIVITY OF BANACH ALGEBRAS WITH DERIVATIONS

被引：13

作者：

Ali, Shakir ^{[1
]}

Khan, Abdul Nadim ^{[2
]}

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia

[2] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2015年 / 91卷 / 03期

关键词：

Banach algebra; derivation;

D O I：

10.1017/S0004972715000118

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to discuss the commutativity of a Banach algebra A via its derivations. In particular, we prove that if A is a unital prime Banach algebra and A has a nonzero continuous linear derivation d : A -> A such that either d((xy)(m)) - x(m)y(m) or d((xy)(m)) - y(m)x(m) is in the centre of A for an integer m = m(x, y) and sufficiently many x, y, then A is commutative. We give examples to illustrate the scope of the main results and show that the hypotheses are not superfluous.

引用

页码：419 / 425

页数：7

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