Sorting ListView in WPF

I tried to sort my listview like this: http://ift.tt/18Sdmq4

XAML:

<ListView x:Name="lvComputers" HorizontalAlignment="Left" Height="440" Margin="10,43,0,0" VerticalAlignment="Top" Width="560" SelectionChanged="lvComputers_SelectionChanged">
            <ListView.View>
                <GridView>
                    <GridViewColumn Width="120" DisplayMemberBinding="{Binding computerName}">
                        <GridViewColumn.Header>
                            <GridViewColumnHeader Tag="Computername" Click="lvComputersColumnHeader_Click">Computername</GridViewColumnHeader>
                        </GridViewColumn.Header>
                    </GridViewColumn>
                    <GridViewColumn Width="80" DisplayMemberBinding="{Binding operatingSystem}">
                        <GridViewColumn.Header>
                            <GridViewColumnHeader Tag="Betriebssystem" Click="lvComputersColumnHeader_Click">Betriebssystem</GridViewColumnHeader>
                        </GridViewColumn.Header>
                    </GridViewColumn>
                </GridView>
            </ListView.View> 
        </ListView>

C#:

  private void loadComputers()
        {
            lvComputers.ItemsSource = mainController.getComputers();
            lvComputers.Items.SortDescriptions.Add(new SortDescription("Computername", ListSortDirection.Ascending));
            CollectionView view = (CollectionView)CollectionViewSource.GetDefaultView(lvComputers.ItemsSource);
            view.SortDescriptions.Add(new SortDescription("Computername", ListSortDirection.Ascending));
            view.Filter = UserFilter;  

        }

 private void lvComputersColumnHeader_Click(object sender, RoutedEventArgs e)
        {
            GridViewColumnHeader column = (sender as GridViewColumnHeader);
            string sortBy = column.Tag.ToString();
            if (listViewSortCol != null)
            {
                AdornerLayer.GetAdornerLayer(listViewSortCol).Remove(listViewSortAdorner);
                lvComputers.Items.SortDescriptions.Clear();
            }

            ListSortDirection newDir = ListSortDirection.Ascending;
            if (listViewSortCol == column && listViewSortAdorner.Direction == newDir)
                newDir = ListSortDirection.Descending;

            listViewSortCol = column;
            listViewSortAdorner = new SortAdorner(listViewSortCol, newDir);
            AdornerLayer.GetAdornerLayer(listViewSortCol).Add(listViewSortAdorner);
            lvComputers.Items.SortDescriptions.Add(new SortDescription(sortBy, newDir));
        }

"getComputers" returns a list of computers based on this class:

public class Computers
    {
        public String computerName { get; set; }
        public String operatingSystem { get; set; }
    }

UserFilter is for a searchbox. But for some reason the sorting wont work.

I tried to add this

lvComputers.Items.SortDescriptions.Add(new SortDescription("Computername", ListSortDirection.Ascending));

to

loadComputers();

but it doesnt work either.

what am i doing wrong?