We have more of a communal philosophy in our home. Everything is free for everyone. There has been a FEW things that are this person's or that person's. But, usually it is, "nothing is yours or mine, it is ours". The reasoning for this is because we have children that can eventually wear each other clothing. The toys are communal, but usually, they deal with what is their age level. If the child buys it, then it is theirs. Only the boys have "their" room, out of necessity. But, it is still our house.
It has been easier with each child to share, since they have never known any different. Since oldest DS was in daycare for a while, we never had a sharing issue. However, there is usually an issue with the next older sibling taking from the younger toddler just to hear them scream.

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I think that he is pretty young to really understand sharing. Teach him sympathy, and when the baby gets upset that her toy was taken, he will likely hand it back to her. Trading is always a good option. Some retraining will be the best approach if you want them to successfully share and get along over the long haul. And, it will be a good for him as he gets older.
Although, you could always give him the "boy toys" and get her "girl toys" and then they have a His and Hers situation, and no squabbles are necassary. Although, I say that with tongue in cheek, because that would fly like a brick around here.

My 20 mo old boy loves baby dolls as much as he likes his trash truck, and he REALLY likes trash trucks. LOL
It will get better as he is likely to play with her more than just beside her, then they can roll the ball back and forth and the like. That teaches sharing and taking turns. You might help her do this with him, and then he can learn the concept. Kymberli