Ok ... let's say I have an elven dagger and I improve it through smithing to legendary.

then I enchant it, will I be able to use arcane blacksmith to improve it anymore or once it's legendary pre - enchantment it stays that way?

Assuming you've raised or fortified your smithing from when it was first brought to legendary... yes.

I'm confused ... it was my bad though with how I arranged my question.

elven dagger

smithed to legendary (no enchantment)

enchant it with fire damage

can it now be improved any more through smithing?

edit: the reason I ask, I'm trying to decide if I need anything beyond steel and arcane blacksmith on the smithing tree.

You can improve enchanted items with Arcane Smithing.

elven dagger

smithed to legendary

enchant it with fire damage

try to improve it more with smithing

you can, but your smithing didn't improve, so how are you going to improve it more?

you get better at smithing by drinking fortify smithing potion or wearing fortify smithing gear

try to improve your legendary elven dagger more with smithing

yes you can

Not unless your Skill in Snithing goes up after you brought the Elven Dagger to Legendary.\

Arcane Blacksmith gives you the ability to improve magical armor and weapons, it doesn't confer any bonuses on its own.

With out the Perk, you can do nothing with magical items. The Perk just lets you improve enchanted weapons and armor, but adds no bonuses to your improvement calculations.

Without Arcane Smithing you can not improve enchanted items. With arcane smithing you can improve a enchanted items. It doesn't change how much they can be improved. You can always further improve and item through smithing you just need raise your smithing skill or fortify it further. Legendary has no cap.

ok, that's what I was looking for. I think I asked the question wrong initially. I just didn't want to invest too many perks in smithing, and since arcane and (let's say) elven don't add together I'll just get arcane.

Remember that without the perk you can only improve the item half as much. Your legendary steel dagger will deal signifcantly more damage then your elven dagger because you already have steel smithing.

so if I have elven smithing and arcane and a elven dagger I can improve it to legendary once with elven and then again to legendary with arcane (after enchanting)?

No!. All arcane smithing does it let you improve magic items it doesn't change how much they can be improved. It doesn't matter what order you enchant it/improve it in. Elven smithing DOES change how much you can improve elven weapons and armor all arcane smithing does is let you improve the magical ones.

Example I have 100 in smithing, I can improve an elven weapon by 10 points of damage.(15 with my fortify gear on) If I take elven smithing I can improve it by 15 points of damage.(29 points with my fortify smithing gear).
All arcane smithing would do is let me improve the item after its been enchanted say if I get even more powerful fortify smithing gear.