Simple autoloader, but trying to make it psr-compliat
Well, your class is psr-1 compliant. But i think you mean psr-0. 

To have a maximum compliance to the psr-0 autoloader. simply copy paste it...

Your method for instance doesn't work for Class_Name

if you call your autoload with \namespace\ClassName the first \ doesn't get trimmed. This will leed to problems. (php will load /path/to/lib//namespace/ClassName.php)

as mentioned in the comments, the use of the $this->dirSeparatorSymbol is weird. You don't need it. so don't use it.

Edit: 'unused' namespace

Often you will have multiple libraries at different places. Your own will probably reside under ROOT.'/lib/' but other libraries you downloaded should/will be under ROOT.'/vendor/AwesomeLibrary/src/'. to accomodate this. You will register 2 autoloaders:

$personalLoader = new ClassLoader\Loader('Personal','/lib/');
$personalLoader->register();

$awesomeLoader = new ClassLoader\Loader('AwesomeLibrary','/vendor/AwesomeLibrary/src/');
$awesomeLoader->register();

Now your autoloader should check or it is allowed to load the file. For instance if I use
AwesomeLibrary/MyClass; the personal loader shouldn't do anything since it knows nothing about AwesomeLibrary. the second awesomeLoader however knows how to load the AwesomeLibrary.