Operator algebras associated with multiplicative convolutions of arithmetic functions

doi:10.1007/s11425-017-9281-0

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	Operator algebras associated with multiplicative convolutions of arithmetic functions
	Dong, Aiju 1,2; Huang, Linzhe 3,4; Xue, Boqing3
	2018-09-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	61 期号:9 页码:1665-1676
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.
关键词	natural numbers arithmetic functions C*-algebra von Neumann algebra differential operator
DOI	10.1007/s11425-017-9281-0
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000442229900009
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31078
专题	数学所
通讯作者	Xue, Boqing
作者单位	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
推荐引用方式 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.