REPRESENTASI GELFAND-NAIMARK-SEGAL DARI ALJABAR-C^*

    Senjaya, Ihsan Wira (2013) REPRESENTASI GELFAND-NAIMARK-SEGAL DARI ALJABAR-C^*. S1 thesis, Universitas Pendidikan Indonesia.

    Abstract

    Aljabar-C^* adalah suatu aljabar Banach dengan syarat-syarat tambahan. Adanya sifat dari aljabar-C^* yang tidak dimiliki oleh aljabar Banach umum membuktikan bahwa struktur dari aljabar-C^* lebih kaya daripada aljabar Banach umum. Suatu subaljabar-* tutup dari B(H) disebut aljabar-C^* konkret. Melalui suatu representasi, setiap aljabar-C^* abstrak dapat dikaitkan dengan aljabar-C^* konkret. Salah satu teknik standar dalam mengkonstruksi representasi dari aljabar-C^* A adalah melalui fungsional linear positif f pada A. Dari fungsional linear positif ini dikonstruksi subruang vektor N dari A yang selanjutnya dapat dikonstruksi ruang hasilkali dalam H_f yang diperoleh dari kuosien A/N. Kemudian diperoleh pengaitan π_f:A⟶B(H_f). Tripel (A,H_f,π_f) selanjutnya disebut representasi Gelfand-Naimark-Segal dari A.
    Kata kunci: aljabar-C^*, B(H), fungsional positif, representasi.

    A C^*-algebra is a Banach algebra with additional properties. The existence of that properties, makes the structure of C^*-algebras is better than general Banach algebras. We say closed *-subalgebra of B(H) is concrete C^*-algebra. Through a representation we can associate an abstract C^*-algebra with the concrete C^*-algebra. One of the standard techniques for constructing a representation of C^*-algebra A is through a positive linear functional f on A. We can construct a vector subspace N of A and an inner product space H_f which is obtained from quotient space A/N, and then we have π_f:A⟶B(H_f). We write (A,H_f,π_f) for the triple we constructed, it is called Gelfand-Naimark-Segal representation associated to f.
    Keyword: C^*-algebras, B(H), positive functional, representation.

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    Item Type: Thesis (S1)
    Subjects: Universitas Pendidikan Indonesia > Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Matematika - S1 > Program Studi Pendidikan Matematika
    Divisions: Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Matematika - S1 > Program Studi Pendidikan Matematika
    Depositing User: Riki N Library ICT
    Date Deposited: 27 Aug 2013 07:18
    Last Modified: 27 Aug 2013 07:18
    URI: http://repository.upi.edu/id/eprint/341

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