operatoralgebrasassociatedwithmultiplicativeconvolutionsofarithmeticfunctions

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	operatoralgebrasassociatedwithmultiplicativeconvolutionsofarithmeticfunctions
	Dong Aiju 1; Huang Linzhe 2; Xue Boqing2
	2018
发表期刊	sciencechinamathematics
ISSN	1674-7283
卷号	61 期号:9 页码:1665
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.
语种	英语
资助项目	[National Natural Science Foundation of China] ; [Natural Science Basic Research Plan in Shaanxi Province of China]
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/49036
专题	数学所
作者单位	1.西安文理学院 2.中国科学院数学与系统科学研究院
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.