#### Approximation properties and vector integrals in banach spaces = Banach 공간의 근사성질과 벡터 적분

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This thesis is devoted to study of characterizations of approximation properties and the weak Radon-Nikodym property in Banach spaces and various properties of the Lebesgue space \$L^P(G)\$ of real valued measurable functions which are integrable with respect to a vector measure \$\textsl{G}\$. First, we establish new necessary and sufficient conditions for Banach spaces to have the approximation property. We modify the proof of Grothendieck for dual Banach spaces to have the approximation property. And we also add some properties and relations of a weak version of the approximation property. Secondly, we introduce Grothendieck`s method of relating the metric approximation property to tensor products, we establish another sufficient condition for dual spaces to have the metric approximation property. We also characterize the weak Radon-Nikodym property which is a candidate for another sufficient condition for dual spaces to have the metric approximation property. Finally, we investigate various properties of the Lebesgue space \$L^P(G)\$. And we also study conditions on \$\textsl{G}\$ which enables \$L^1(G)\$ to enjoy the property of the classical Lebesgue space. In particular, we show, by an example, that \$L^1(G)\$ does not have the approximation property in general.
Choi, Chang-Sun최창선
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2009
Identifier
309277/325007  / 020037428
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2009.2, [ iii, 58 p. ]

Keywords

approximation properties; the weak Radon-Nikodym property; vector measures; Lebesgue spaces; 근사성질; 약한 라돈 니코딤 성질; 벡터 측도; 르베그 공간; approximation properties; the weak Radon-Nikodym property; vector measures; Lebesgue spaces; 근사성질; 약한 라돈 니코딤 성질; 벡터 측도; 르베그 공간

URI
http://hdl.handle.net/10203/41913