...
namespace Project1.DataSource
{
  public class SourceManager
  {
    public DataTable DataTable1;

    ...
  }
}
...

<Window 
    x:Class="Project1.UI.Window1"
    xmlns:c="clr-namespace:Project1.DataSource;assembly=Project1.DataSource"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="" Height="385" Width="618" >
  
  <Window.Resources>
    <c:MySourceManager x:Key="SourceManager"/>
  </Window.Resources>

  <Grid x:Name="MyGrid">
    <ListView ItemsSource="{Binding DataTable1}" IsSynchronizedWithCurrentItem="True">
      <ListView.DataContext>
        <Binding Source="{StaticResource MySourceManager}"/>
      </ListView.DataContext>
      <ListView.View>
        <GridView>
          <GridViewColumn DisplayMemberBinding="{Binding Path=Name}" Header="Name" Width="100"/>
        </GridView>
      </ListView.View>
    </ListView>
  </Grid>
</Window>

...
  
  <Window.Resources>
    <c:SourceManager x:Key="MySourceManager"/>
  </Window.Resources>

...