Abstract :
Suatu pemetaan pada ruang vektor khususnya ruang bernorma disebut operator. Salah satu kajian tentang operator, dalam hal ini operator linear, merupakan suatu operator yang bekerja pada ruang barisan. Banyak kasus pada operator linear dari ruang barisan ke ruang barisan dapat diwakili oleh suatu matriks takhingga. Matriks takhingga yaitu suatu matriks yang berukuran takhingga kali takhingga.
Sebagai contoh, suatu matriks A : l_(3 )? l_(3?2),dengan A=[?(a_11&a_12& ?@a_21&a_22& ?@?&?&?)],
l_3={x=(x_i )?|(?_(i=1)^??|x_i |^3 )^(1/3)?}, dan l_(3?2)={x=(x_i )?|(?_(i=1)^??|x_i |^(3/2) )^(2/3) ?} merupakan barisan bilangan real. Selanjutnya dikontruksikan operator A dari ruang barisan? l?_3 ke ruang barisan l_(3?2) dengan basis standar {e_k } dengan e_k=(0,0,?,1_((k)),?) dan ditunjukkan bahwa koleksi semua operator membentuk ruang banach.
Kata Kunci : Operator, Ruang Barisan Terbatas
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The mapping of vector space, especially on norm space is called operator. One of the cases about the operator, in case of linear operator, is the operator which works on sequence space. There aremany cases in the linear operator from one sequence space to another which can be represented by infinite matrices. The infinite matrices are the matrices which sized infinite times infinite.
for A : l_(3 )? l_(3?2),where A=[?(a_11&a_12& ?@a_21&a_22& ?@?&?&?)],l_3={x=(x_i )?|(?_(i=1)^??|x_i |^3 )^(1/3)?}, and l_(3?2)={x=(x_i )?|(?_(i=1)^??|x_i |^(3/2) )^(2/3) ?} is a sequence real numbers. Furthermore, it can be constructed an operator A from finite sequence space l_(3 ) to sequence space l_(3?2) 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