| Banach代数上同态的自动连续性 |
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| 引用本文： | 曹怀信. Banach代数上同态的自动连续性[J]. 陕西师范大学学报(自然科学版), 1989, 0(4) |
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| 作者姓名： | 曹怀信 |
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| 作者单位： | 陕西师大数学系 |
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| 基金项目： | 陕西师范大学青年科学基金 |
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| 摘 要： | 本文引入了具有性质OUDP的Banach代数A,证明了从A到任一Banach代数的任一同态自动连续.对有单位的Banach代数A,证明了从A到任一Banach代数的满同态自动连续当且仅当从矩阵代数M_n(A)到任一Banach代数的满同态自动连续.同时还证明:若从A(M_n(A))的任一闭双理想出发的同态自动连续,则从M_n(A)(A)的任一闭双理想出发的满同态的分离空间由拟幂零元组成.
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| 关 键 词： | Banach代数 同态 自动连续性 |
Automatic Continuity of Homomorphisms on Banach Algebras |
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| Cao Huaixin. Automatic Continuity of Homomorphisms on Banach Algebras[J]. Journal of Shaanxi Normal University: Nat Sci Ed, 1989, 0(4) |
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| Authors: | Cao Huaixin |
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| Affiliation: | Department of Mathematics |
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| Abstract: | In this paper, the Banach algebra with the property OUDP is defined and it is proved that every homomorphism from such algebra into a Banach algebra is continuous. For an unit Banach algebra A, it is shown that every homomorphism from A is continuous if and only if so does it from M_n(A) and that if each homomorphism from every closed bi-ideal of A(resp. M_n(A)) is continuous, then the separating space of a homomorphism from a closed bi-ideal of M_n(A)(resp.A ) onto a Banach algebra B consists of qusi-nilpotent elements of B. |
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| Keywords: | Banach algebra homomorphism automatic continuity |
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