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,w...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.展开更多
基金supported in part by UCM(Grant No.PR3/23-30811)。
文摘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.
