Interpolation of Closed Ideals of Bilinear Operators

We extend the（outer） measure γI associated to an operator ideal I to a measure γI for bounded bilinear operators. If I is surjective and closed, and J is the class of those bilinear operators such that γI（T） = 0, we prove that J coincides with the composition bideal I ? B. If I satisfies the Σr-condition, we establish a simple necessary and sufficient condition for an interpolated operator by the real method to belong to J. Furthermore, if in addition I is symmetric, we prove a formula for the measure γI of an operator interpolated by the real method. In particular, results apply to weakly compact operators.