Boundedness and Spec trum of Multiplicative Convolution Operators Induced by Arithmetic Functions

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	Boundedness and Spec trum of Multiplicative Convolution Operators Induced by Arithmetic Functions
其他题名	Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions
	Kibrom GEBREMESKEL 1; Lin Zhe HUANG 1
	2019
发表期刊	数学学报:英文版
ISSN	1439-8516
卷号	35.0 期号:008 页码:1300-1310
摘要	In this paper, we consider a multiplicative convolution operator Mf acting on a Hilbert spaces l^2(N,ω;). In particular, we focus on the operators M1 and Mμ, where μ, is the Mobius function. We investigate conditions on the weight ω under which the operators M1 and Mμ are bounded. We show that for a positive and completely multiplicative function f,M1 is bounded on l^2(N, f^2) if and only if \|\|f\|\|1 1. As an application, we obtain some results on the spectrum of M1^M1 and M^μMμ. Moreover, von Neumann algebra generated by a certain family of bounded operators is also considered.
其他摘要	In this paper, we consider a multiplicative convolution operator M_f acting on a Hilbert spaces ?~2( N, ω ). In particular, we focus on the operators M_1 and M_μ, where μ is the Mobius function. We investigate conditions on the weight ω under which the operators M_1 and M_μ are bounded. We show that for a positive and completely multiplicative function f, M_1 is bounded on ?~2( N, f~2) if and only if ‖f‖_1 1. As an application, we obtain some results on the spectrum of M_1~* M_1 and M_μ~* M_μ. Moreover, von Neumann algebra generated by a certain family of bounded operators is also considered.
关键词	Arithmetic functions Mobius function von Neumann algebra
收录类别	CSCD
语种	中文
资助项目	[Templeton Religion Trust] ; [Chinese Academy of Sciences]
CSCD记录号	CSCD:6538831
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/55459
专题	中国科学院数学与系统科学研究院
作者单位	1.中国科学院数学与系统科学研究院 2.Department of Mathematics, College of Natural and Computational Sciences, Aksum University, Aksum, Tigray, Ethiopia
推荐引用方式 GB/T 7714	Kibrom GEBREMESKEL,Lin Zhe HUANG. Boundedness and Spec trum of Multiplicative Convolution Operators Induced by Arithmetic Functions[J]. 数学学报:英文版,2019,35.0(008):1300-1310.
APA	Kibrom GEBREMESKEL,&Lin Zhe HUANG.(2019).Boundedness and Spec trum of Multiplicative Convolution Operators Induced by Arithmetic Functions.数学学报:英文版,35.0(008),1300-1310.
MLA	Kibrom GEBREMESKEL,et al."Boundedness and Spec trum of Multiplicative Convolution Operators Induced by Arithmetic Functions".数学学报:英文版 35.0.008(2019):1300-1310.