Does cooldown reduction influence item abilities?

Solution 1:

No, your cooldown reduction (CDR) items will not effect your item cooldowns.

Cooldown reduction does not apply on item active abilities such as that of Deathfire Grasp or item passive effects with cooldowns such as that of Guardian Angel. Most sources of cooldown reduction also does not apply on summoner spells unless specifically stated, e.g. the unique enchantment effect of Distortion for boots or the unique passive, Aid, of Eleisa's Miracle. Cooldown Reduction does not apply to an Innate Ability [the passive abilities of Champions] of any kind.

However, you can get the utility tree mastery Artificer to reduce the cooldown times of your item's active effects by by 7.5/15%. This can make a pretty significant difference on some of the longer cooldowns.

Source: League of Legends Wikia