ARTHA KURNIA ALAM, 1317031010 (2017) REPRESENTASI OPERATOR LINIER PADA RUANG BARISAN l4. FAKULTAS MATEMATIKA DAN ILMU PENGETAAHUAN ALAM, UNIVERSITAS LAMPUNG.
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Abstrak
Suatu pemetaan pada ruang vektor khususnya ruang bernorma disebut operator. Banyak kasus pada operator linier dari ruang barisan ke ruang barisan dapat diwakili oleh suatu matriks tak hingga. Sebagai contoh, suatu matriks A∶l_4→l_4 dengan A=[■(a_11&a_12&…@a_21&a_22&…@⋮&⋮&⋮)] and l_4={x=(x_i )├|(∑_(i=1)^∞▒|x_i |^4 )^(1/4)<∞ ┤} merupakan barisan bilangan real. Selanjutnya, dikonstruksikan operator A dari ruang barisan l_4 ke ruang barisan l_4 dengan basis standar (e_k ) dan ditunjukan 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. 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_4→l_4 where A=[■(a_11&a_12&…@a_21&a_22&…@⋮&⋮&⋮)] and l_4={x=(x_i )├|(∑_(i=1)^∞▒|x_i |^4 )^(1/4)<∞ ┤} is a sequence real numbers. Furthermore, it can be constructed an operator A from sequence space l_4 to sequence space l_4 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: | 15113066 . Digilib |
| Date Deposited: | 03 Oct 2017 07:46 |
| Last Modified: | 03 Oct 2017 07:46 |
| URI: | http://digilib.unila.ac.id/id/eprint/28404 |
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