Interpolation of Closed Ideals of Bilinear Operators  

作　　者：Fernando Cobos Luz M.Fernandez-Cabrera Anton Martinez 

机构地区：[1]Departamento de Analisis Matematico y Matematica Aplicada,Facultad de Matematicas,Universidad Complutense de Madrid,Plaza de Ciencias 3,28040 Madrid,Spain [2]Seccion Departamental del Departamento de Analisis Matematico y Matematica Aplicada,Facultad de Estudios Estadιsticos,Universidad Complutense de Madrid,28040 Madrid,Spain [3]Departamento de Matematica Aplicada I,Escuela de Ingenierιa Industrial,Universidad de Vigo,36200 Vigo,Spain

出　　处：《Acta Mathematica Sinica,English Series》2025年第1期209-230,共22页数学学报(英文版)

基　　金：supported in part by UCM(Grant No.PR3/23-30811)。

摘　　要：We extend the(outer)measureγ_(I) associated to an operator ideal I to a measureγ_(I) for bounded bilinear operators.If I is surjective and closed,and J is the class of those bilinear operators such thatγ_(I)(T)=0,we prove that J coincides with the composition bideal I?B.If I satisfies theΣ_(r)-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 measureγ_(I) of an operator interpolated by the real method.In particular,results apply to weakly compact operators.

关 键 词：Measures associated to bideals of operators real interpolation measure of weak noncompactness of a bilinear operator adjoint operator of a bilinear operator 

分 类 号：O177[理学—数学]