Many of the books you get from a public library are DRM books. That is they have Digital Rights Management in them. The library loans them to you for a period and at the end of that period they expire on your PC. (Even if you have not finished them.) Since the library only buys a specific number of copies of each title they cannot allow people to keep them forever.
I would be surprised if you were able to convert the library PDF files to another format or even get them to open on your Sony Reader.
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