I am currently reading a history book written by a professor of history at an American University. I have noticed that the sources cited by the professor are frequently the professors own previous works. Is this considered appropriate in academic literature?
Yes, that's a very common practice in academic literature. If you're someone who has published multiple papers/articles/books/etc., you're probably writing most of that about the same, or at the very least, very similar topics. As such, much of what you do in each new paper is improve upon what you've learned before in your previous research, so it's important to draw on that past research to help substantiate your new research and help your readers understand the connections you're making by knowing where in your past writings to look if they want to read more on that specific topic.
Self-citation is not only normal, but often encouraged by the historical community. The rationale behind this is that not citing yourself can result in self-plagiarism. Without this citation, it becomes difficult to parse out what is new research or ideas and what the author has worked on. While there are extreme cases, a historian who references their own work excessively should raise some read flags, this procedure is the norm.
Furthermore, most professional historians tend to work in stages and a history book is often a cumulative process. They typically present papers on their research at conferences, publish articles in peer-reviewed journals and anthologies before collecting that information into a book. The ideas and research at each stage are significantly different enough, often by virtue of format (conference papers can be quite different than articles) to merit a citation.