Extension of polynomials, complex convexity and M-ideal properties of Banach function spaces = Banach 함수 공간에서 다항식의 확장, 복소 볼록성과 M-ideal 성질

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This thesis is devoted to a study of various geometric properties of Banach function spaces, relations with each other and its applications. First, we study the effect of M-ideal properties and complex convexity to extension of polynomials. In particular, we show when order continuous subspace of Marcinkiewicz spaces has M-ideal properties in its bidual and we find the relation between the complex extreme points and extension of 2-homogeneous polynomials in order continuous subspace of complex Marcinkiewicz sequence spaces. Secondly, we find the necessary and sufficient conditions for complex convexity of Orlicz-Lorentz spaces. Using complex convexity, we show that the norm-attaining subspace $NA(d_*(w,1), d(w,1))$ is not dense in $L(d_*(w,1), d(w,1))$ if and only if $w ∈ ℓ_2$ in the complex case. Finally, we deal with complex convexity, monotonicity, cotype of Banach lattices. With these results, we obtain the following results: a K$ö$the-Bochner function space E(X) is strictly (resp. uniformly) complex convex if and only if E is strictly (resp. uniformly) monotone and X is strictly (resp. uniformly) complex convex.
Advisors
Choi, Chang-Sun최창선
Description
한국과학기술원 : 응용수학전공,
Publisher
한국과학기술원
Issue Date
2004
Identifier
240544/325007  / 020015230
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 응용수학전공, 2004.8, [ iv, 94 p. ]

Keywords

COMPLEX CONVEXITY; 함수 공간; M-IDEAL PROPERTIES; FUNCTION SPACE; EXTENSION OF POLYNOMIALS; 복소 볼록성; M-ideal 성질; 다항식의 확장

URI
http://hdl.handle.net/10203/41877
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=240544&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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