My book jacket covers have been glued to the book!

Hi, have you tried to warm up the glue at all? A hairdryer or press with a warm iron through extra paper may soften it?

Good luck

"A hairdryer or press with a warm iron through extra paper may soften it?"

Be careful with the iron! After totally screwing up some documents, I learned that using scrap paper isn't sufficient enough to protect through the iron. Use baking paper (baking parchment? It has several names. Either way, it's sold in kitchen supplies.). Some ink is heat activated and will come right off! I gummed up an iron really bad when I forgot to put the baking paper between the page and the iron. Whoops! Same thing happened when I was trying to save money and use scrap paper instead of buying baking parchment. Once the ink gets on your iron, it will transfer back onto the page and smear all over the place. If you gum up your iron, you can clean with vinegar water. Works like a charm.

I know that doesn't help the OP, but I wanted to share my oops so that it isn't repeated!

The heat answers are good and if it was really attached with a heat activated glue then heat will help with the separation. 

That said, in your case, with the limited amount of time that Public Libraries have to deal with books in circulation I might also suggest that removing the covers by scraping them off the paste-down and then ameliorating the paste-down might be the way to go. This is a sort of rip-off-the-bandage approach. You can test the attachment and see what happens when you start pulling it off. Sometimes only a light layer of the paste-down will come off and if it is a plain end-paper then that isn't so bad. A book repair knife or lifting knife would help. https://saveyourbooks.com/product-category/book-repair-supplies/

Can you include a photo or two of the problem area?

I attached two pictures. One has just the paper side of the book jacket cover glued, but the other is the actual book jacket that is glued to the inside cover of the book. I have not tried heat, but I do have wax paper so I will definitely try an iron.  Right now I have been trying to gently pull the cover back, but it is stuck tight.

I tried the iron, but I did not have much success. I was able to at least get most of the book jackets off and ended up scraping off as much of the paper from the cover as I could. The spots were recovered when I put the new book jacket and cover back on. The more I look at them the more I think hot glue was used. Now I am running into the actual book jacket being glued to the inside of the book and nothing will loosen it without ripping the book jacket.

To be clear, do not use Waxed Paper with the Iron to reactivate and remove glue! You want to use Baking Parchment / Silicone Release Paper with heat. If you use Waxed Paper with heat you will transfer the wax into the paper and it won't ever come out completely. Just like trying to remove crayon from a book. 

Sometimes, when dust jacket paper is stuck like this to a board it is possible to split the dust jacket paper and only remove a layer of it. However, if the glue has soaked through into the paper then there is no help for it. The best you could do to preserve the dust jacket (without taking it to a conservation lab) is to err on the side of removing paper from the board side. Once the DJ is free there may be more possible.

Sometimes, when dust jacket paper is stuck like this to a board it is possible to split the dust jacket paper and only remove a layer of it. However, if the glue has soaked through into the paper then there is no help for it. The best you could do to preserve the dust jacket (without taking it to a conservation lab) is to err on the side of removing paper from the board side. Once the DJ is free there may be more possible.