Gebremeskel Kibrom G; Huang Linzhe
Source Publicationactamathematicasinicaenglishseries
AbstractIn this paper, we consider a multiplicative convolution operator Mf acting on a Hilbert spaces l(2)(N,omega). In particular, we focus on the operators M1 and M mu, where mu is the Mobius function. We investigate conditions on the weight omega under which the operators M1 and M mu 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 parallel to f parallel to(1) 1. As an application, we obtain some results on the spectrum of M1 M1 and M mu M mu. Moreover, von Neumann algebra generated by a certain family of bounded operators is also considered.
Funding Project[Templeton Religion Trust] ; [Chinese Academy of Sciences]
Document Type期刊论文
Recommended Citation
GB/T 7714
Gebremeskel Kibrom G,Huang Linzhe. boundednessandspectrumofmultiplicativeconvolutionoperatorsinducedbyarithmeticfunctions[J]. actamathematicasinicaenglishseries,2019,35(8):1300.
APA Gebremeskel Kibrom G,&Huang Linzhe.(2019).boundednessandspectrumofmultiplicativeconvolutionoperatorsinducedbyarithmeticfunctions.actamathematicasinicaenglishseries,35(8),1300.
MLA Gebremeskel Kibrom G,et al."boundednessandspectrumofmultiplicativeconvolutionoperatorsinducedbyarithmeticfunctions".actamathematicasinicaenglishseries 35.8(2019):1300.
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