Operator algebras associated with multiplicative convolutions of arithmetic functions | |
Dong, Aiju1,2; Huang, Linzhe3,4; Xue, Boqing3 | |
2018-09-01 | |
Source Publication | SCIENCE CHINA-MATHEMATICS |
ISSN | 1674-7283 |
Volume | 61Issue:9Pages:1665-1676 |
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. |
Keyword | natural numbers arithmetic functions C*-algebra von Neumann algebra differential operator |
DOI | 10.1007/s11425-017-9281-0 |
Language | 英语 |
Funding Project | National Natural Science Foundation of China[11371290] ; National Natural Science Foundation of China[11701549] ; Natural Science Basic Research Plan in Shaanxi Province of China[2017JM1045] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000442229900009 |
Publisher | SCIENCE PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31078 |
Collection | 数学所 |
Affiliation | 1.Xian Univ, Dept Math, Xian 710065, Shaanxi, Peoples R China 2.Beijing Normal Univ, Fac Educ, Beijing 100875, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
Recommended Citation GB/T 7714 | Dong, Aiju,Huang, Linzhe,Xue, Boqing. Operator algebras associated with multiplicative convolutions of arithmetic functions[J]. SCIENCE CHINA-MATHEMATICS,2018,61(9):1665-1676. |
APA | Dong, Aiju,Huang, Linzhe,&Xue, Boqing.(2018).Operator algebras associated with multiplicative convolutions of arithmetic functions.SCIENCE CHINA-MATHEMATICS,61(9),1665-1676. |
MLA | Dong, Aiju,et al."Operator algebras associated with multiplicative convolutions of arithmetic functions".SCIENCE CHINA-MATHEMATICS 61.9(2018):1665-1676. |
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