Tuesday 11/10, Manuel Gonz<strong>á</strong>lez

[kubis at math.cas.cz]

 ------------------------------------------------------------------------- 

 Tuesday 11th October, 10:00am 
 ------------------------------------------------------------------------- 

 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 .