Banach空间C[a,b]中的再赋范

Renorming in Banach Space C[a,b]

Banach空间C[a,b]在通常的最大值范数意义下,不具有严格凸性质和依测度收敛的Opial性质,根据C[a,b]的特点,赋适当的范数,使它具有严格凸性质和依测度收敛的Opi al性质及(* )性质.

C,‖·‖)does not have the strictly convex property and the Opial property in meature, where‖x‖= maxt∈|x(t)|; C is properly renormed such that it has the above two properties and (*) property.