REPRESENTASI OPERATOR LINIER DARI RUANG BARISAN TERBATAS l_13 KE RUANG BARISAN TERBATAS l_(13/12)

AMANDA YONA NINGTYAS , 1417031008 (2017) REPRESENTASI OPERATOR LINIER DARI RUANG BARISAN TERBATAS l_13 KE RUANG BARISAN TERBATAS l_(13/12). FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM, UNIVERSITAS LAMPUNG.

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Abstrak

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 tak hingga. Matriks tak hingga yaitu suatu matriks berukuran tak hingga kali tak hingga. Sebagai contoh, suatu matriks A : l_(13 )→ l_(13⁄12), dengan A=[■(a_11&a_12& …@a_21&a_22& …@⋮&⋮&⋮)],l_13={x=(x_i )├|(∑_(i=1)^∞▒|x_i |^13 )^(1/13)<∞┤}, dan l_(13⁄12)={x=(x_i )├|(∑_(i=1)^∞▒|x_i |^(13/12) )^(12/13)<∞ ┤} merupakan barisan bilangan real. Selanjutnya dikontruksikan operator A dari ruang barisan l_13 ke ruang barisan l_(13⁄12) 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 ABSTRACT 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 are many 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 example, a matrices A : l_(13 )→ l_(13⁄12), where A=[■(a_11&a_12& …@a_21&a_22& …@⋮&⋮&⋮)],l_13={x=(x_i )├|(∑_(i=1)^∞▒|x_i |^13 )^(1/13)<∞┤}, and l_(13⁄12)={x=(x_i )├|(∑_(i=1)^∞▒|x_i |^(13/12) )^(12/13)<∞ ┤} is a sequence real numbers. Furthermore, it can be constructed an operator A from finite sequence space l_(13 ) to sequence space l_(13⁄12) 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

Tipe Karya Ilmiah: Skripsi
Subyek: Q Science (General) > QA Mathematics
Program Studi: Fakultas MIPA > Prodi Matematika
Depositing User: 82735086 . Digilib
Date Deposited: 05 Jan 2018 02:16
Last Modified: 05 Jan 2018 02:16
URI: http://digilib.unila.ac.id/id/eprint/29728

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