Limited users are granted full control of their own files. Admins should be granted full control of all files. Permissions work like this: What are permissions?
So the only way, using permissions, for someone to compress a file is if they had the 'modify' permission, if I am to understand it correctly. But they can likely delete the file as well.
You might test this yourself to see what happens when you limit specific permissions (You can change it back if it doesn't work). Create a restore point just in case. Here is what KingSovereign
wrote about it:
quote from microsoft website: Changing multiple file permissions? - Microsoft Answers
In order to change multiple permissions at once you must first obtain ownership of the directory that contains the files that you need to change permissions for (do this by right-clicking the Drive (not the one that windows is installed on), folders, etc > Properties > then click the Security tab > then look towards the bottom right hand side and click "Advanced" > then click the Owner tab > then click Edit > then find your username under "Change owner to:" > then make sure that the checkbox next to "Replace owner on subcontainers and objects" is checked > then click Apply)
Then click OK until all property windows are closed. Then:
Right-click the same directory, folder, or file > click Advanced (next to "For special permissions or advanced settings click Advanced") > click Change Permissions > click Add... > enter your username in the box (under "Enter the object names to select") > click OK > check the box (next to "Replace all child object permissions with inheritable permissions from this object") > click Apply > Then click OK (to exit out of all property windows)
THIS HAS ONLY BEEN TESTED ON WINDOWS 7 ULTIMATE (I cannot attest to other versions)
Personally, if I were a limited user, I would hate for someone else to be compressing my files. The best ways to save disk space are to defragment the drive, uninstall programs that aren't needed, Limit disk space for things like paging file (though not too much), offline files, and system restore points. Here is a good tutorial on all of these things by Brink
: Optimize Windows 7
I don't know of a way to give a user the specific ability to compress a file. I think changing permissions for this may be too hard to even be worth it.
If someone somehow gets permission to compress other people's files, how do they access the files? limited users might not be able to see other users files to begin with.\
As the admin, you would have more success in this endevour. Using the quote above, you could compress whole files in different user accounts.