The answer to that is both yes and no.  NO you can’t look into anyone’s Akashic Records without their permission or request.  

If anyone thinks they are in someone else’s record without permission, the information you are given won’t necessarily be valid. No matter what the intention, going into someone else’s energy field (or trying to) without their permission is never a good idea.  Your Akashic Records are part of your energy field so thereby protected from harm by your guides, angels, helpers and spiritual teachers on the other side.  

As for the yes part, if you are looking at your Akashic Records and someone else is involved in your experience, you can see that information only to the extent it involves you.

The best piece of advice is “mind your own vibration!”  Always look at raising your vibration and stop worrying about anyone else and what they may or may not be doing. You control you and so do they.