APLIKASI PRINSIP KURVA TUTUP

Abstract

In this paper we study the use of the closed graph principle applied to direct sum closed subspace of a Banach Space. We will first discuss the concept of a closed graph described in  the form of theorem or principle. The properties of closed linear mapping  related to the concept of a closed graph will also be explained in detail in the  form of two lemmas. In order to prove the  closed graph principle we utiliize an  open mapping principle. The objective of this study is to show that each  direct sum of a closed subspace will exactly resulted one linear mapping that has  a property of bounded projection. Our results show that a uniqueness of bounded projection on Banach Space can always be obtained from direct sum of two closed subspace. Furthermore, open mapping can be generated  from  premise of a closed graph having certain  conditions