Hi Ronnie ..
You won't be able to update the apps download from the Apple ID used by the previous owner.
Just ignore those updates from the App Store.
Content downloaded using one Apple ID cannot be transferred to another Apple ID and Apple ID's cannot be merged.
What you need to do is purchase the apps using your Apple ID.
Thanks for your reply
But all the apps that needs to be updated are visible and in function on the Imac, even when I am using it under my own Apple ID on the Imac
Does that mean that I can use the apps as they are, but not have them updated unless I purchase them or download them by myself?
In addition to the apps, did the iMac originally come with Lion (as shown in your profile) or did the seller upgrade to it? If Lion was the originally installed OS, then there is no problem. If it was an upgrade, then that OS version is also not transferable and is tied to the original purchaser's Apple ID forever. That means you will never be able to reinstall the OS if needed (which may become necessary if there is a problem and Lion does not come with install disks).
The best way would be to wipe the drive as suggested, reinstall the original OS, update and/or upgrade and then purchase your own apps using your own Apple ID for everything.