The calculus of one-sided M-ideals and multipliers in operator spaces

The theory ofM-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 Neu-mann algebra. If in addition X is an operator A–B-bimodule for C∗-algebras A and B, then the module operations onX 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. 1. Introduction. It has long been recognized that the algebraic structure of a C∗-algebra A is closely linked to its geometry as a Banach space (see [25]). This principle was illustrated in [5], and [2], p. 237, where it was shown that the close