%0 Journal Article
%A Cobos Díaz, Fernando
%A Fernández-Cabrera Marín, Luz María
%A Martínez, Antón
%T Interpolation of closed ideals of bilinear operators
%D 2024
%U https://hdl.handle.net/20.500.14352/113343
%X We extend the (outer) measure $\gamma_{_{\mathcal{I}}}$ associated to an operator ideal  $\mathcal{I}$ to a measure  $\gamma_{_{\mathfrak{I}}}$ for bounded bilinear operators. If $\mathcal{I}$ is surjective and closed, and $\mathfrak{I}$ is the class of those bilinear operators such that $\gamma_{_{\mathfrak{I}}}(T)=0$, we prove that $\mathfrak{I}$ coincides with the composition bideal $\mathcal{I}\circ \mathfrak{B}$. If $\mathcal{I}$ satisfies the  $\Sigma_r$-condition, we establish a simple necessary and sufficient condition for an interpolated operator by the real method to belong to $\mathfrak{I}$. Furthermore, if in addition $\mathcal{I}$ is symmetric, we prove a formula for the measure  $\gamma_{_{\mathfrak{I}}}$ of an operator interpolated by the real method. In particular, results apply to weakly compact operators.
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