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The Positive Operators on Banach Lattices
Author: JingHui
Tutor: ChenZiLi
School: Southwest Jiaotong University
Course: Basic mathematics
Keywords: Banach lattice AM compact operator o- weakly compact operator Lattice homomorphism Order Continuous Norm sigma - laterally complete Can be divided into the nature of Can interpolation
CLC: O177.2
Type: Master's thesis
Year: 2009
Downloads: 26
Quote: 0
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Abstract
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AM- compact operator sub- o - weak of compact operator , the lattice homomorphism the Banach lattice three categories very important operator , this article explains the historical background and prior knowledge , discuss and study the AM- compact operator decomposition , o - weak of compact operators sub- AM- tight operator relationship , and in the same state of decomposition , mainly: the first part of a brief exposition of the relevant historical background and prior knowledge , the reproduction of numerous mathematical predecessors in outstanding work , which is the theoretical foundation and basis. The second section discusses AMο compact operator by c 0 < / sub > the closed subspace decomposition problem that E is a Banach lattice its conjugate E ' orderly continuous norm , F is a Banach lattice so that it conjugate space F ' have strongly ordered units , each AM- compact operator T : E → F are by c 0 < / sub > the closed subspace Z to break down , and T = RS R, S is AM- compact operator . third part focuses on the o - weak of compact operators with AM- compact operator for any Banach lattice F Banach lattice E is a sigma - laterally complete Banach lattice , each from E to F o - weakly compact operator AM- tight discussed in section IV the Banach lattice grid homomorphic decomposition E is separable , F has a countable interpolation , V : E → G is a lattice homomorphism positive linear mapping S : G → F , each continuous linear operator T : E → F meet T ≤ S V decomposed into T = S 1 < / sub > · V S 1 < / sub > : G → F is linear and the 0 ≤ the S 1 < / sub > ≤ S.
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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Banach spaces and their linear operator theory.
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