KEKONVERGENAN LEMAH PADA RUANG HILBERT

    Mubarak, Moch Ramadhan (2017) KEKONVERGENAN LEMAH PADA RUANG HILBERT. S1 thesis, Universitas Pedidikan Indonesia.

    Abstract

    Penelitian ini mengkaji mengenai kekonvergenan lemah pada ruang Hilbert atas lapangan
    real. Kekonvergenan lemah termotivasi oleh kekonvergenan kuat sehingga terdapat
    beberapa sifat dari kekonvergenan kuat yang berlaku pada kekonvergenan lemah seperti
    ketunggalan limit, kelinearan limit, dan keterbatasan suatu barisan. Keterkaitan antara
    konvergen kuat dan lemah mengakibatkan terdapat pendefinisian dan sifat-sifat dari
    barisan Cauchy lemah dan himpunan kompak secara barisan dan secara lemah. Di akhir
    pembahasan dibicarakan mengenai keberlakuan Teorema Bolzano-Weierstrass pada ruang
    Hilbert. ---------This study discusses the weak of convergence in Hilbert space over the real field. The weak
    of convergence is motivated by a strong convergence as a result that there are some
    properties of the strong convergence which is applicable in the weak of convergence such
    as uniqueness of limit, linearity of limit, and boundedness of a sequence. The relationship
    between strong and weak convergent implies that there are the definition and properties of
    weak Cauchy sequence and weakly compact set. In the end of the discussion discussed
    about the generalize of Bolzano-Weierstrass theorem in Hilbert space

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    Official URL: http://repository.upi.edu
    Item Type: Thesis (S1)
    Additional Information: No. Panggil: S MAT MOC k-2017; Pembimbing: I. Encum Sumiaty, II. Cece Kustiawan; NIM: 1200365
    Uncontrolled Keywords: Ruang Hilbert, konvergen kuat, konvergen lemah, himpunan kompak secara barisan dan secara lemah, teorema Bolzano-Weiertrass.
    Subjects: L Education > L Education (General)
    Q Science > QA Mathematics
    Divisions: Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Matematika - S1
    Depositing User: Mrs. Santi Santika
    Date Deposited: 05 Mar 2019 07:14
    Last Modified: 05 Mar 2019 07:14
    URI: http://repository.upi.edu/id/eprint/34022

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