Weak approximation properties in banach spaces = Banach 공간에서의 약한 근사성질들

This thesis is devoted to an investigation of various approximation properties in Banach spaces, relations between these properties, and various topologies on the space of operators. First, we introduce various weak approximation properties, which are in general weaker than known approximation properties, and establish necessary and sufficient conditions for Banach spaces to have those properties. And we study inheritances of those properties from the dual space of a Banach space to the Banach space and vice versa. Secondly, we study if one approximation property implies another. By providing elaborate examples we prove that some properties is strictly stronger than others. We also observe that for dual spaces or reflexive spaces more properties turn out to be equivalent. Finally, we consider various locally convex vector topologies on the space of bounded linear operators on Banach spaces and investigate their topological properties, including compactness. We then apply the results to our study of the approximation properties.
Advisors
Choi, Chang-Sunresearcher최창선researcher
Publisher
한국과학기술원
Issue Date
2007
Identifier
263487/325007  / 020025076
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 응용수학전공, 2007.2, [ iii, 81 p. ]

Keywords

approximation property; 근사성질

URI
http://hdl.handle.net/10203/41894
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=263487&flag=t
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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