Hadi, Raden Muhammad (2015) BIMODUL-C* HILBERT. S1 thesis, Universitas Pendidikan Indonesia.
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Abstract
Misalkan A dan B aljabar-C* dan X ruang vektor kompleks. Modul-C* Hilbert kanan X_A (kiri (_B^)X) adalah modul yang dilengkapi dengan hasil kali dalam kanan ⟨∙,∙⟩_A (kiri (_B^)⟨∙,∙⟩ ) dan lengkap dalam norm modul kanan ‖∙‖_A(kiri (_B^)‖∙‖ ) sedangkan bimodul-C* Hilbert (_B^)X_A adalah bimodul yang dilengkapi dengan hasil kali dalam kanan dan kiri juga lengkap dalam norm modul kanan dan kiri. Tujuan dari penulisan skripsi ini adalah untuk mengetahui bagaimana mengkonstruksi modul-C* Hilbert dan Bimodul-C* Hilbert, mempelajari sifat-sifat serta memberi contoh. Penelitian dilakukan dengan cara studi literatur, yaitu dengan mempelajari pokok bahasan yang berhubungan dengan modul-C* Hilbert. Berdasarkan hasil yang diperoleh, bimodul-C* Hilbert dapat dikonstruksi melalui modul dengan skalarnya adalah dua aljabar-C* yang dilengkapi dengan hasil kali dalam dan memenuhi sifat kelengkapan dalam norm modul. Selain itu, akan dijelaskan bagaimana cara mengaplikasikan modul-C* Hilbert melalui contoh. Kata kunci: Modul, bimodul, aljabar-C*, ruang Hilbert, ruang hasil kali dalam, modul-C* Hilbert, bimodul-C* Hilbert. Let A and B C*-algebras and X complex vector space. Right (left) Hilbert-C* module X_A ((_B^)X) is a module that completed with right (left) inner product ⟨∙,∙⟩_A ((_B^)⟨∙,∙⟩ ) and satisfied completeness on right (left) norm module ‖∙‖_A ((_B^)‖∙‖ ) whereas Hilbert-C* bimodule (_B^)X_A is bimodule that completed with right and left inner product and satisfied completeness on right and left norm module. Objectives of this final paper are to how to construct it, studied its properties along with its application by examples. Research was done by literatures study, that is studied its main themes that highly related with Hilbert-C* module and Hilbert-C* bimodule. As the result, Hilbert-C* bimodule can be constructed through module with two C*-algebras as scalar completed with inner product and satisfies completeness on norm module. Then, we will show its application by examples. Keyword: Module, bimodule, C*-algebra, Hilbert space, inner product space, Hilbert-C* module, Hilbert-C* bimodule.
| Item Type: | Thesis (S1) |
|---|---|
| Additional Information: | No. Panggil : S MAT HAD b-2015; Pembimbing : I. Rizky Rosjanvardi, II. Isnie Yusnitha |
| Uncontrolled Keywords: | Modul, bimodul, aljabar-C*, ruang Hilbert, ruang hasil kali dalam, modul-C* Hilbert, bimodul-C* Hilbert. |
| Subjects: | L Education > L Education (General) Q Science > QA Mathematics |
| Divisions: | Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Jurusan Pendidikan Matematika > Program Studi Pendidikan Matematika |
| Depositing User: | Mrs. Neni Sumarni |
| Date Deposited: | 11 Mar 2016 03:19 |
| Last Modified: | 11 Mar 2016 03:19 |
| URI: | http://repository.upi.edu/id/eprint/19528 |
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