HILBERT SPACE IN SEQUENCE SPACE l2

Alwi, Wahidah ( Jurusan Matematika FST-UIN Alauddin)

Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA)
Vol 2, No 1 (2014)

The main object of the vectors are the vectors can be added together and generate a vector, and produces a number is multiplied by another vector. Any set of objects with properties like this are called "vector space". In this study aims to assess pre-Hilbert space and Hilbert space in a sequence space 2  . Based on the purpose of the study, it was found that a vector space form a pre Hilbertspace when equipped with the inner product space. While a pre-Hilbert space is complete if every Cauchy sequence (xn) in X, convergent in X called a Hilbert space.