2026-06-01T02:02:24Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/1133432025-03-18T13:17:31Zcom_20.500.14352_14col_20.500.14352_15

Interpolation of closed ideals of bilinear operators Cobos Díaz, Fernando Fernández-Cabrera Marín, Luz María Martínez, Antón Measures associated to bideals of operators Real interpolation measure of weak non-compactness of a bilinear operator Adjoint operator of a bilinear operator Ciencias 12 Matemáticas 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. Universidad Complutense de Madrid Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE unpub 2025-01-08T16:37:34Z 2025-01-08T16:37:34Z 2024 journal article AM https://hdl.handle.net/20.500.14352/113343 XXXX-XXXX eng PR3/23-30811 embargoed access application/pdf Springer