  The theory of M-ideals and multiplier mappings of Banach spaces naturally
generalizes to left (or right) M-ideals and multiplier mappings of operator
spaces. These subspaces and mappings are intrinsically characterized in terms
of the matrix norms. In turn this is used to prove that the algebra of left
adjointable mappings of a dual operator space X is a von Neumann algebra. If in
addition X is an operator A--B-bimodule for $C^{*}$-algebras A and B, then the
module operations on X are automatically weak$^{*}$ continuous. One sided
L-projections are introduced, and analogues of various results from the
classical theory are proved. An assortment of examples is considered.
