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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dc.contributor.advisorChoi, Chang-Sun-
dc.contributor.advisor최창선-
dc.contributor.authorLee, Han-Ju-
dc.contributor.author이한주-
dc.date.accessioned2011-12-14T04:39:53Z-
dc.date.available2011-12-14T04:39:53Z-
dc.date.issued2004-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=240544&flag=dissertation-
dc.identifier.urihttp://hdl.handle.net/10203/41877-
dc.description학위논문(박사) - 한국과학기술원 : 응용수학전공, 2004.8, [ iv, 94 p. ]-
dc.description.abstractThis 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.eng
dc.languageeng-
dc.publisher한국과학기술원-
dc.subjectCOMPLEX CONVEXITY-
dc.subject함수 공간-
dc.subjectM-IDEAL PROPERTIES-
dc.subjectFUNCTION SPACE-
dc.subjectEXTENSION OF POLYNOMIALS-
dc.subject복소 볼록성-
dc.subjectM-ideal 성질-
dc.subject다항식의 확장-
dc.titleExtension of polynomials, complex convexity and M-ideal properties of Banach function spaces = Banach 함수 공간에서 다항식의 확장, 복소 볼록성과 M-ideal 성질-
dc.typeThesis(Ph.D)-
dc.identifier.CNRN240544/325007 -
dc.description.department한국과학기술원 : 응용수학전공, -
dc.identifier.uid020015230-
dc.contributor.localauthorChoi, Chang-Sun-
dc.contributor.localauthor최창선-
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