MASALAH NORM MINIMUM PADA RUANG HILBERT DAN APLIKASINYA

Abstract

In this paper, will be discussed about the minimum norm in the pre- Hilbert Space, Hilbert space and its modification, and its application.  The results are: Let  X  be  a  pre-Hilbert space and  M is a sub space of X.   If an element  is fixed, then : . If there is   such that   , then   is unique. Let  H be a Hilbert space and M  be a closed sub space of  H . If   , then there is  a unique element   such that  ,  . Let X  be a Hilbert  space ,  M  be a closed  sub space of X . If  V =x+ M, for an element xX, then there is a unique element of    such that  ,    M.Key words : minimum norm,  pre-Hilbert space, Hilbert space , orthogonality