Banach-Kantorovich C*-algebras and zero-two laws for positive contractions /
In this thesis, we study C^*-algebras over Arens algebras. Moreover, we consider C^*-algebra of sections and will prove that C^*-algebra over L^ω is isometrically *-isomorph to C^*-algebra L^ω (Ω,X). Furthermore, we investigate the state space of C^*-algebras over L^ω. We also study dominated oper...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
Kuantan, Pahang :
Kulliyyah of Science, International Islamic University Malaysia,
2017
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| Subjects: | |
| Online Access: | Click here to view 1st 24 pages of the thesis. Members can view fulltext at the specified PCs in the library. |
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| Summary: | In this thesis, we study C^*-algebras over Arens algebras. Moreover, we consider C^*-algebra of sections and will prove that C^*-algebra over L^ω is isometrically *-isomorph to C^*-algebra L^ω (Ω,X). Furthermore, we investigate the state space of C^*-algebras over L^ω. We also study dominated operators acting on Banach-Kantorovich L_p-lattices. Further, using the methods of measurable bundles of Banach-Kantorovich lattices, we prove the strong zero-two law for the positive contractions of the Banach-Kantorovich lattices L_p (∇,m). After that, we illustrate an application of the methods used in previous study to prove a result related to dominated operators. Thereafter, we collect some necessary well-known facts about non-commutative L_1-spaces. Then we prove an auxiliary result about dominant operators. Next, we prove a generalized uniform "zero-two" law for multi-parametric family of positive contractions of the non-commutative L_1-spaces. Furthermore, we recall necessary definitions about L_1 (M,Φ) – the non-commutative L_1-spaces associated with center valued traces and we show auxiliary result about the existence of the non-commutative vector-valued lifting. Finally, we prove that every positive contraction of L_1 (M,Φ) can be represented as a measurable bundle of positive contractions of non-commutative L_1-spaces, and this allows us to establish a vector- valued analogue of the uniform "zero-two" law for positive contractions of L_1 (M,Φ). |
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| Physical Description: | x, 80 leaves : illustrations ; 30cm. |
| Bibliography: | Includes bibliographical references (leaves 75-78). |