Frodo actually manages to bring out the good in Gollum after a while. The books says that he started calling himself Smeagol, and he said "I" rather than "we". So Frodo (and I think also Gandalf) was right that there was some good at the bottom of all the evilry the Ring had brought forth. But as noldor says, Smeagol stops trusting Frodo when they're at the forbidden pool , and Gollum gets hold of him again, and Smeagol changes back to who he was when Frodo and Sam first met him.

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by Lembas