三角Banach代数上的对偶模Jordan导子和对偶模广义导子
Dual module Jordan derivations and dual module generalized derivations of triangular Banach algebra

摘要： 设A,B是含单位元的Banach代数, M是一个Banach A,B-双模。 T=(A MB) 按照通常矩阵加法和乘法,范数定义为‖(a mb)‖=‖a‖A+‖m‖M+‖b‖B,构成三角Banach代数。通过作用(f hg)(a mb)=f(a)+h(m)+g(b), T的对偶空间 T*为(A* M*B*)。 在T*上定义模作用 (a mb)·(f hg)=(a·f+m·h b·hb·g), (f hg)·(a mb)=(f·a h·ah·m+g·b), 使其成为一个对偶Banach T-双模。从T到T*的映射称为对偶模映射。 本文对T上对偶模Jordan导子和对偶模广义导子进行讨论, 给出了T上对偶模Jordan导子是对偶模导子的一个充分条件并且对T上对偶模广义导子进行了刻画。
Abstract: Let A and B be unital Banach algebras, and let M be a Banach A, B-bimodule. Then T=(A MB) becomes a triangular Banach algebra when equipped with the usual matrix operation and a Banach space norm ‖(a mb)‖=‖a‖A+‖m‖M+‖b‖B. T*=(A* M*B*) is the dual space of T by the action (f hg)(a mb)=f(a)+h(m)+g(b). T* becomes a dual Banach T- bimodule with the module action defined by am (a mb)·(f hg)=(a·f+m·h b·hb·g), (f hg)·(a mb)=(f·a h·ah·m+g·b). The map from T into T* is called dual module map. We investigate the dual module Jordan derivations and dual module generalized derivations on T, giving a condition under which a dual module Jordan derivation is a dual module derivation and a characterization of dual module generalized derivation