operatoralgebrasassociatedwithmultiplicativeconvolutionsofarithmeticfunctions | |
Dong Aiju1; Huang Linzhe2; Xue Boqing2 | |
2018 | |
Source Publication | sciencechinamathematics |
ISSN | 1674-7283 |
Volume | 61Issue:9Pages:1665 |
Abstract | 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. |
Language | 英语 |
Funding Project | [National Natural Science Foundation of China] ; [Natural Science Basic Research Plan in Shaanxi Province of China] |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/49036 |
Collection | 数学所 |
Affiliation | 1.西安文理学院 2.中国科学院数学与系统科学研究院 |
Recommended Citation 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. |
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