C([0.1]) 위에서의 개양선형 범함수 = Almost Positive Linear Functionals on C([0.1])

다국어 초록 (Multilingual Abstract)

■ Contents
In this paper two almost positive linear functionals Φ+and Φ(a,b) were constructed by means of an almost positive linear functional on C(M). Similarly for the positive linear functionals, it is shown that an almost positive linear functional Φ has a decomposition Φ=Φ+-Φ-. Finally some relative boundnesses are found.
■ Research Results
(1) Suppose that C0(M) is container in a vector lattice LB. If Φ+(f) = ***** where □C0 (M)f□LB then the functional Φ+ is defind on LB and linear.
(2) If Φ is an almost positive linear functional defined on a vector lattice LB which contains C0 ([0.1]) then Φ= Φ+ - Φ- where Φ+ is a positive linear functional and Φ - is an almost positive one respectively.
(3) || Φ || = Φ+ (e)+ Φ-(e)
(4) An almost positive linear functional Φ(a,b) was constructed by means of limit in Φ, and then it can be shown that Φ+ and Φ(a,b) are relatively bounded.

목차 (Table of Contents)

• 제1장 서론
• 제2장 Φ+와 그의 기본 성질
• 제1절 예비정리
• 제2절 양함수에 대한 Φ+(f+g) = Φ+(f)+Φ+(g)
• 제3절 확장과 분해
• 제3장 개선형범함수 Φ(a,b)와 상대 유계성
• 제1절 Φ(a,b)의 정의와 상대 유계성
• 참고문헌