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Operator algebras associated with multiplicative convolutions of arithmetic functions
Dong, Aiju1,2; Huang, Linzhe3,4; Xue, Boqing3
2018-09-01
Source PublicationSCIENCE CHINA-MATHEMATICS
ISSN1674-7283
Volume61Issue:9Pages:1665-1676
AbstractThe 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.
Keywordnatural numbers arithmetic functions C*-algebra von Neumann algebra differential operator
DOI10.1007/s11425-017-9281-0
Language英语
Funding ProjectNational 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 AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000442229900009
PublisherSCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31078
Collection数学所
Affiliation1.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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