%A 1217031075 Angger Pambudhi
%T REPRESENTASI OPERATOR PADA RUANG BARISAN TERBATAS l_5
%X Suatu pemetaan pda ruang vector khususnya ruang bernorma disebut operator. Banyak kasus pada operator linear dari ruang barisan dapat diwakili oleh suatu matriks tak hingga. Sebagai contoh, suatu matriks A= l_5  ? l_5  dengan A=[?(a_11&a_12&?@a_21&a_22&?@?&?&?)] dan l_5={x=(x_i )?|(?_(i=1)^??|x_i |^5 )^(1/5)<? ?} merupakan barisan bilangan real. Selanjutnya, dikonstruksikan operator A dari ruang barisan l_5 ke ruang barisan l_5 dengan basis standar {e_k} dan ditunjukkan bawa koleksi semua operator membentuk ruang Banach.

Kata Kunci : Operator, ruang barisan terbatas 



ABSTRACT

The mapping of vector space especially on norm space is called operator. There are many cases in linear operator from sequence space into sequence space can be represented by an infinite matrices. For example, a matrices A?l_5?l_5 where A=[?(a_11&a_12&?@a_21&a_22&?@?&?&?)] and l_5={x=(x_i )?|(?_(i=1)^??|x_i |^5 )^(1/5)<? ?} is a sequence real numbers. Furthermore, it can be constructed an operator A from sequence space l_5 to sequence space l_5 by using a standard basis (e_k ) and it can be proven that the collection all the operators become Banach space.

Key Words :  Operator, finite sequence space

%C UNIVERSITAS LAMPUNG
%D 2017
%I FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM 
%L eprints25214