ON SOME FUNCTIONAL EQUATIONS ON STANDARD OPERATOR ALGEBRAS

被引:3
|
作者
Kosi-Ulbl, Irena [1 ]
Vukman, Joso [2 ]
机构
[1] Univ Maribor, Fac Mech Engn, SLO-2000 Maribor, Slovenia
[2] Univ Maribor, Dept Math & Comp Sci, FNM, SLO-2000 Maribor, Slovenia
关键词
Prime ring; semiprime ring; Banach space; standard operator algebra; BICIRCULAR PROJECTIONS; DERIVATIONS; RINGS; SPACES;
D O I
10.3336/gm.44.2.11
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The main purpose of this paper is to prove the following result. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators on X, let Lambda(X) subset of L(X) be a standard operator algebra, and let T:A(X) -> L(X) be an additive mapping satisfying the relation T(A(2n+1)) -Sigma(2n+1)(i=1)(-1)(i+1)A(i-1)T(A)A(2n+1-i), for all A is an element of A(X) and some fixed integer n >= 1. In this case T is of the form T(A) = AB+BA, for all A is an element of A(X) and some fixed B is an element of L(X). In particular, T is continuous.
引用
收藏
页码:447 / 455
页数:9
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