[blockquote]Water can be split into peroxide and oxygen[/blockquote]

No it can't.

Water is H2O
peroxide is H2O2
oxygen is O2

Both oxygen and peroxide have excess oxygen and a deficit of hydrogen compared to water.

Water can be split into hydrogen and oxygen or to the OH radical and atomic oxygen. These products can then be either seperated from or recombined with the parent mass of water to produce other chemical species.

IF you find a way to seperate out, liberate, or consume the hydrogen then clearly you can produce both peroxide and molecular oxygen from a mass of water, but the nett redox reaction is zero, since the hydrogen is equally as reducing as the oxidants are oxidising...