Probably not. The copyright in the emails belongs to the author, which in this case is the person who sent you the emails. The fact that someone sends you an email or posts something on the Internet does not mean that they have given up their copyright rights. The classic case involves J.D. Salinger, the author of Catcher in the Rye, among other books. He sent his friends beautifully composed letters. Someone collected the letters and published them as a book. Salinger sued for copyright infringement and won. Then that person published a new book paraphrasing the emails. Salinger sued again and won again.
Now as I keep saying, every case is fact specific. It may be that under the particular facts of your case you would have the right to publish the email under some theory of law such as implied license. But based on your limited recital of facts, this does not seem likely.
This answer is not intended to be a substitute for personalized legal advice. I have presented only an overview of the legal issues. There are many nuances and some exceptions to general legal principles. Real problems are very fact based.. If you have a specific legal problem, you should consult an attorney. You can find more useful information on my law firm website resources page at www.marshallcomputer.com or you can contact me directly at firstname.lastname@example.org or (206) 524-0655.
As Mr. marshall stated, the author of the email owns the rights to the email (unless there is some highly unlikely written or implied license between you and the author giving you thoe right to publish thse works)
You say the person who sent you the emails would have no interest in publishing them. Is this no interest in publishing them, or no interest in whether or not they were published? I ask because if the author did not care whether they were published or not, then it would be highly likely that he would give you permission to publish the emails, but if he would not want them published, then you have next to zero chance of publishing them without facing serious legal issues. (Note: this continues to be true even if the author dies, as the copyrights continue for 75 years after the death of the author and are part of the author's estate, ownership of the copyright passing to his heirs.)
Finally, regardless of the copyright laws, there are many other issues that should be reveiwed by legal counsel prior to publishing.
My disclaimer is simply that Avvo already has an adequate disclaimer.
The author owns the work unless there is a contract to the contrary. While there may be case-specific facts that affect the answer to your question, generally one must seek consent before publishing the work of others.
I am an attorney in Pennsylvania but I am not currently *your* attorney. Nothing in my communication should be construed as creating an attorney/client relationship. Please contact me if you wish to retain me as your counsel.