Israel's Action Against Hamas: A Just War?

I don't have a lot to say about this. Just a quick thought:

   It seems clear that Israel meets the conditions required for jus ad bellum: it has just cause to go to war against Hamas. In fact, it is merely responding to Hamas's act of war against it.

   The only interesting question is whether Israel's actions meet the conditions required for jus in bello--i.e. whether it is conducting the war in a just way. My inclination, based on what I think I know, is to think that the answer is in the affirmative. The pro-Palestinian (mostly) left seems to disagree--that seems to be the upshot of their appeals to e.g. the number of children that have been killed. The argument seems, roughly, to be: if so many children are killed, Israel cannot be conducting the war justly. (Though, of course, sometimes they seem to be sidling up to the claim that if any children are killed, Israel cannot be conducting the war justly... But I'll ignore that here.)

   My entire life I have inclined toward a pro-Israel position. I realize that I'm not exactly neutral. But I also realize that I don't know enough about how Israel is conducting the war to know that they are conducting it justly. Furthermore, some technical knowledge about military matters (beyond what little I know) is required in order to answer the question adequately. And this is not to mention that just war theory gets complicated, and it isn't my area of specialization. We hear stories about "roof knocking" to alert the occupants of buildings that it's going to be bombed, and this seems, to me, as if it is almost beyond the call of duty. But at this point I am reduced to guesses about what can be done, what is being done, and what is required.

   My view is that Israel is acting with remarkable restraint. But I also realize that I may have no right to be too sure about that.