| C［a,b］上半范数的两个问题 |
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| 引用本文： | 刘修生.C［a,b］上半范数的两个问题[J].山东大学学报(理学版),2006,41(5):84-86. |
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| 作者姓名： | 刘修生 |
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| 作者单位： | 黄石理工学院数理学院,湖北,黄石,435003 |
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| 摘 要： | R上无限维交换代数．研究了C［a,b］上面的半范数Np(f(x))=［∫ba|f(x)|pdx］1p(0＜p＜∞)与半模N∞(f(x))=maxaxb［|f(x)|］的关系，通过这种关系证明了Np(f(x))对0＜p＜∞不是C［a,b］上的稳定半范数．给出了C［a,b］上不是连续半模的一个实例．
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| 关 键 词： | 半范数 半模 范数 稳定半范数 幂结合代数 |
| 文章编号： | 1671-9352（2006）05-0084-03 |
| 收稿时间： | 2005-09-27 |
| 修稿时间： | 2005年9月27日 |
Two problem of the subnorms on C[a,b] |
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| LIU Xiu-sheng.Two problem of the subnorms on C[a,b][J].Journal of Shandong University,2006,41(5):84-86. |
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| Authors: | LIU Xiu-sheng |
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| Institution: | School of Math, and Physics, Huangshi College of Technology, Huangshi 435003, Hubei, China |
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| Abstract: | 〖GK2*2]Abstract: Let C［a,b］ be a set of all real valued continuous function on ［a,b］. It is an infinite dimensional commutive algebra with regard to general function operations(scalar multiplication, addition and multiplication). A relation has been studied between subnorms Np(f(x)) and submodulus N∞［f(x)］. Based on this relationship, it proves that Np(f(x)) are not stable subnorms for 0＜p＜∞. Finally, an example of discontinuous submodules on C［a,b］ is given. |
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| Keywords: | subnorms submodule norms stable subnorms power-associative algebra |
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