No, you can't.

Even if you could they could still see your listings if they weren't logged in.

Your listings are there for the world to see

If fhere is a serious reason why you do not want someone to see your listings, report them to eBay.

for example, if you have received threats or abusive communications from them.

then eBay could look into it and possibly deregister their account...

but anyone can browse, so it won't stop them looking, but if they have been a problem, then they could be prevented from being an issue for someone else. If it is harassment of some form that is behind your question.