Is this sentence acceptable? It sounds correct but looks informal.
Usually, historical nonfiction works are not the most exciting books that one can read, but Jack’s surprisingly rises above the rest.
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Just to be clear, possessive pronouns come in two forms. The first are often called possessive adjectives or possessive determiners: my, our, your, his, her, its, and their. They function as adjectives and come before nouns: my house, his shoes, their car. The second forms are called independent or absolute possessives: mine, ours, yours, his, hers, its and theirs. They function as nouns and can stand alone as a subject or object of a verb: mine is on the table, the book is yours. (Note that none of the independent possessives mentioned above use an apostrophe to show possession).
In your case I see no possessive pronoun and nothing "informal" either. It sounds correct and it looks correct.