Almost convergence and Euler totient matrix
type: Item
instance of: scholarly article
title: Almost convergence and Euler totient matrix
zbMATH Open document ID: 1453.46004
author: Serkan Demiriz
author: Merve İlkhan
author: Emrah Evren Kara
published in: Annals of Functional Analysis
publication date: 2020-07-17T00:00:00Z
review text: The \(\Phi\)-transform of complex-valued sequences is defined by \[ v_{n}=\sum_{k\mid n}\varphi( k) u_{k},\ n\in\mathbb{N}, \] where \(\varphi\) denotes the Euler totient function. Let \[ \widehat{c}\left(\Phi\right) :=\left\{(u_{k})\biggm\vert\exists\alpha\in\mathbb{C}:\lim_{m\rightarrow\infty}\sum_{j=0}^{m}\frac{v_{n+j}}{m+1}=\alpha\text{ uniformly in }n\right\}. \] From the authors' abstract: ``It is proved that the space \(\widehat{c}\left(\Phi\right)\) and the space of all almost convergent sequences are linearly isomorphic. Further, the \(\beta\)-dual of the space \(\widehat{c}\left(\Phi\right)\) is determined and Euler totient core of a complex-valued sequence has been defined. Finally, inclusion theorems related to this new type of core are obtained.''
reviewed by: Toivo Leiger
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 7222413
zbMATH Keywords: Euler function
zbMATH Keywords: Euler totient matrix
zbMATH Keywords: almost convergence
zbMATH Keywords: core theorems
MaRDI profile type: Publication
full work available at URL: s43034-019-00041-0
OpenAlex ID: W2994289821
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DOI: 10.1007/S43034-019-00041-0
description: scientific article; zbMATH DE number 7222413