Abstract:

This article presents a novel method to prove that: let E be an AM-space and if dim E≥ 3, then there does not exist any odd subtractive isometric mapping from the unit sphere S(E) into $S[L(\Omega,\mu)]$. In particular, there does not exist any real linear isometry from E into $L(\Omega,\mu)$.

Key words: Isometric mapping, odd and subtractive mapping, AM-space