Remarks on Duality Mapping and the Lax-Milgram Property

Abstract

Some conditions under which the duality map is a homeomorphism from a Banach space $X$ onto $X\ast$ and upper-semicontinuous at some dense subset of $X$ are derived. Some further pro-perties of the duality mapping are established in connection with the structure of the Banach space $X$. The so-called Lax-Milgram property of the bilinear forms is also investigated.