Tuesday 11/10, Manuel Gonz<strong>á</strong>lez
kubis at math.cas.cz
kubis at math.cas.cz
Thu Oct 6 09:00:01 CEST 2016
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Tuesday 11th October, 10:00am
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Speaker:Manuel González, Universidad de Cantabria, Santander, Spain
Title: Convolution operators on $L_1(G)$ which are tauberian or cotauberian
Abstract
An operator $T:X\to Y$ is said to be \emph{tauberian} when its second conjugate satisfies
$T^{**-1}(Y)=X$, and it is said to be \emph{cotauberian} when $T^*$ is tauberian.
We study the convolution operators $T_\mu$ acting on the group algebras $L_1(G)$, where
$G$ is a locally compact abelian group and $\mu$ is a complex Borel measure on $G$.
We show that $T_\mu$ is Fredholm when it is cotauberian.
Moreover, assuming that $T_\mu$ is tauberian, we show that $T_\mu$ is invertible
when $G$ is non-compact, that $T_\mu$ is Fredholm when it has closed range and $G$
is compact, and in the remaining case when $G$ is compact and $R(T_\mu)$ is not
closed, we prove that $T_\mu$ is Fredholm when the singular continuous part of $\mu$
with respect to the Haar measure on $G$ is zero.
Joint work with Liliana Cely and El\'oi M. Galego (I.M.E. S\~ao Paulo, Brazil).
For more information see the seminar web page at
https://calendar.math.cas.cz/set-theory-and-analysis-actual .
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