To extend any system page you would need to use the alternate files functionality.
First you need to set the EPfEnableAlternateFiles key in the web.config to true. Next create a new folder called edit_ and create the page you want to extend (use the same name, in this case workspace.aspx).
EPiServer will now check for a file in your alternate folder first before it loads it's own version. This also works for the admin and util directories I believe.
To extend functionality in a page, all you should need to do is make your new page inherit from the system page class, then add any custom functionality you like to your new one.
Hope this helps,
Jeremy.
The problem with this, is that I only want to customize the first tab and keep the rest. And since workspace.aspx (Root) is an ordinary page type, I don't see the reason to use shadowing?