Unfortunately there is no way to allow user to edit only specific parts of an item.
I think you need to look at the JED or KED for an extension that offers this functionality.
If you are comfortable with coding, you could create a simple K2 plugin which checks the current user and removes/ disables elements of the item form.
You can find an example plugin here:
getk2.org/extend/extensions/90-example-k2-plugin-for-developers