operatoralgebrasassociatedwithmultiplicativeconvolutionsofarithmeticfunctions
文献类型：期刊论文
| 作者 | Dong Aiju2; Huang Linzhe1; Xue Boqing1
|
| 刊名 | sciencechinamathematics
 |
| 出版日期 | 2018 |
| 卷号 | 61期号:9页码:1665 |
| ISSN号 | 1674-7283 |
| 英文摘要 | The action of a"center dot on l (2)(a"center dot) is studied in association with the multiplicative structure of a"center dot. Then the maximal ideal space of the Banach algebra generated by a"center dot is homeomorphic to the product of closed unit disks indexed by primes, which reflects the fundamental theorem of arithmetic. The C*-algebra generated by a"center dot does not contain any non-zero projection of finite rank. This assertion is equivalent to the existence of infinitely many primes. The von Neumann algebra generated by a"center dot is B(l (2)(a"center dot)), the set of all bounded operators on l (2)(a"center dot). Moreover, the differential operator on l (2)(a"center dot, 1/n(n+1)) defined by acf = mu * f is considered, where mu is the Mobius function. It is shown that the spectrum sigma(ac) contains the closure of {zeta(s)(-1): Re(s) > 1}. Interesting problems concerning ac are discussed. |
| 资助项目 | [National Natural Science Foundation of China] ; [Natural Science Basic Research Plan in Shaanxi Province of China] |
| 语种 | 英语 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/49035]  |
| 专题 | 数学所 |
| 作者单位 | 1.中国科学院数学与系统科学研究院 2.西安文理学院 |
| 推荐引用方式 GB/T 7714 | Dong Aiju,Huang Linzhe,Xue Boqing. operatoralgebrasassociatedwithmultiplicativeconvolutionsofarithmeticfunctions[J]. sciencechinamathematics,2018,61(9):1665. |
| APA | Dong Aiju,Huang Linzhe,&Xue Boqing.(2018).operatoralgebrasassociatedwithmultiplicativeconvolutionsofarithmeticfunctions.sciencechinamathematics,61(9),1665. |
| MLA | Dong Aiju,et al."operatoralgebrasassociatedwithmultiplicativeconvolutionsofarithmeticfunctions".sciencechinamathematics 61.9(2018):1665. |
入库方式： OAI收割
来源：数学与系统科学研究院
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