TEORI DILASI DALAM RUANG HILBERT DAN RUANG BANACH

Surachman, Annisanti (2017) TEORI DILASI DALAM RUANG HILBERT DAN RUANG BANACH. S1 thesis, Universitas Pendidikan Indonesia.

Abstract

Misalkan A adalah aljabar-C* danΦ:A→B(H) adalah pemetaan positif lengkap. Dilasi pada Φ adalah pasangan (π,K) dimana π:A→B(K) adalah homomorfisma-* dan K memuat H sebagai subruang sedemikian sehingga Φ(a)=Pπ(a) |_H untuk setiap P adalah proyeksi dari K ke H. Teorema Dilasi Naimark membahas teori dilasi pada ukuran bernilai operator. Ukuran bernilai operator E:X→B(H) memiliki ruang dilasi Hilbert apabila terdapat ruang Hilbert K, dua buah operator linear terbatas S:H→K dan T:K→H dan ukuran bernilai idempoten F:Σ→B(K) sedemikian sehingga E(B)=SF(B)T untuk setiap B∈X. Ukuran bernilai operator di ruang Banach E∶ Σ→B(X,Y)dikatakan memiliki ruang dilasi Banach Z jika terdapat operator linear terbatas S∶ Z→ Y dan T∶ X → Z dan ruang ukuran bernilai proyeksi (Ω,Σ,F,B(Z)) sedemikian sehingga untuk setiap B∈Σ, E(B)= SF(B)T. Hal ini merupakan perumuman dari Teorema Dilasi Naimark untuk ukuran bernilai operator dan ruang dilasi Hilbert. Let A be a C*-algebra and Φ:A→B(H) be a completely positive map. Adilation of Φ is a pair (π,K) with π:A→B(K) is a *-homomorphism and K containing H as subspace such that Φ(a)=Pπ(a) |_H for any a projection P of K to H. Naimark’s Dilation Theorem tells about dilation theory in operator-valued measure. An operator-valued measure E:X→B(H) has Hilbert dilation space if there is Hilbert space K, bounded linear operators S:H→K and T:K→H and idempotent, operator-valued measure F:Σ→B(K) such that E(B)=SF(B)T for any B∈X. An operator-valued measure E∶ Σ→B(X,Y) in Banach space is said to have a Banach Dilation space Z if there are bounded linear operators S∶ Z→Y and T∶ X→Z and projection-valued measure space (Ω,Σ,F,B(Z)) such that for any B∈Σ, E(B)= SF(B)T. This is a generalization of Naimark’s Dilation Theorem for operator-valued measure and Hilbert dilation space.

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Official URL: http://repository.upi.edu
Item Type: Thesis (S1)
Additional Information: No. Panggil: S MAT SUR t-2017; Pembimbing: I. Rizki Rosjanuari, II, Isnie Yusnitha; NIM:1203125
Uncontrolled Keywords: ukuran bernilai operator, pemetaan positif lengkap, teorema dilasi Naimark, ruang dilasi Hilbert dan ruang dilasi Banach.
Subjects: L Education > L Education (General)
Q Science > QA Mathematics
Divisions: Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Matematika - S1
Depositing User: Mr. Cahya Mulyana
Date Deposited: 28 Aug 2018 01:58
Last Modified: 28 Aug 2018 01:58
URI: http://repository.upi.edu/id/eprint/31274

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