Ambidexterity

Ambidexterity is a notable passive skill that grants increased damage with your main hand weapon and increased attack speed with your off hand weapon.

While it specifically doesn't say while dual wielding it's safe to assume that it's a requirement based on the modifiers.

Version history

Version	Changes
1.3.0	Ambidexterity has been remade into a new unique notable.
1.2.0	Ambidexterity also grants movement speed. The area surrounding the Witch, Shadow and Ranger has been redesigned. Many values have been adjusted.