  This paper proposes a novel approach to quantizing Nambu brackets in
classical mechanics using operator formalism. The approach employs the ``Planck
derivative'' to represent Nambu brackets, from which we derive a commutation
relation for their quantization. Notably, this commutation relation aligns with
that emerging from the T-duality of closed strings in a twisted torus with a
B-field, thereby hinting at a potential connection with Double Field Theory.
