关于矩阵值Lipschitz代数的子代数研究

Researches on subalgebras of matrix-valued Lipschitz algebras

运用算子论与算子代数的方法,讨论了Lipschitz代数Lα(K,Mn(F))和lα(K,Mn(F))上的几种范数的关系;证明了它们是C(K,Mn(F))的含单位的、正则的、自伴的和逆闭的*-子代数;得到了(lα(K,Mn(F)),‖.‖α)是(Lα(K,Mn(F)),‖.‖α)的含单位的、逆闭的子代数.

Using methods of operator theory and operator algebra, some relations of several norms on the Lipschitz algebras L^α（K, Mn（F）） and l^α（K, Mn（F）） are discussed and it is proved that they are all unital regular ＊-subalgebras of the C^＊-algebra C（K,Mn （F））, it is obtained that （l^α（K, Mn（F））, ｜｜·｜｜α .） is a closed and unital inverseclosed subalgebra of （L^α（K, Mn（F））, ｜｜·｜｜α）.