Tauberian convolution operators acting on L₁(G)

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• 作者：Liliana Cely^a ; ^{mlcelyp@unal.edu.co" class="auth_mail" title="E-mail the corresponding author} ; Eló ; i M. Galego^a ; ^{eloi@ime.usp.br" class="auth_mail" title="E-mail the corresponding author} ; Manuel Gonzá ; lez^b ; ^{manuel.gonzalez@unican.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Banach space ; Multiplier ; Tauberian operator ; Convolution operator
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：299-306
• 全文大小：301 K

文摘

We study the convolution operators T_μ$T_{\mu }$ which are tauberian as operators acting on the group algebras 134bd3ce5599b5bd288d5270311" title="Click to view the MathML source">L₁(G)$L_1(G)$, where G is a locally compact abelian group and μ is a complex Borel measure on G. We show that these operators are invertible when G is non-compact, and that they are Fredholm when they have closed range and G is compact. In the remaining case, when G   is compact and R(T_μ)$R(T_{\mu })$ is not assumed to be closed, we prove that T_μ$T_{\mu }$ is Fredholm when the singular continuous part of μ with respect to the Haar measure on G is zero.