Can I ban a specific email from viewing a google document?

Magnolius

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There is one specific email that I want to restrict access to viewing a document of mine on Google Docs. I want all people of all kind to be able to view this document without having to first give them special permission. But I need to be able to set two conditions. First is that the person with the specific email is the only one unable to view this said document. The second is that only people (not specific people, but anyone with a gmail account) who are logged in to their gmail account can view this document, so that the person with the banned email doesn't just log out and try to view the document. Are these two things possible on Google Docs? And if not google docs, is there anywhere else where I can do something like this?
 
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