分離原理及其應用

A separation principle and its applications

陸韋翰(Wei-Han Lu)

指導教授 ： 劉豐哲

國立臺灣大學/理學院/數學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201700955

摘要

此論文研究一個可推得Hahn-Banach等相關定理的分離原理的等價定理。由此，我們為Agnew-Morse定理、交換群上的順從性、Haar integral的存在性提供自然簡潔的證明。可想像的是這個方法也能幫助分析上其他相關的結果。

關鍵字

分離原理 ； 泛涵 ； 線性算子

並列摘要

This thesis studies an analytic variant of a well-known separation principle from which follows Hahn-Banach theorem and many basic theorems in convex analysis. By using this analytic variant, we provide natural and elegant proofs for Agnew-Morse Theorem, the amenability of abelian groups, and the existence of Haar integrals.
It is conceivable that the approach we suggest here might lead to clarification of some results in convex analysis.

並列關鍵字

separation principle ； functional analysis ； linear functional

參考文獻

{1} Agnew, R.P. and A.P. Morse, {it Extension of linear functionals, with application to limits, integrals, measures, and demsities}, An. Math. 39(1938) 20-30.

{2} Banach, S. {it Sur le problème de la mesure}, Fund. Math. 4(1923), 7-33.

{3} ------, {it Théorie des opérations linéaires}, Warszawa, 1932, 27.

{7} Greenleaf, Frederick P. {it Invariant Means on Topological Groups}, New York University(1969).

{8} Hahn, H. {it Über lineare Gleichungssysteme in linearen Räumen}, J. Reine. Angew. Math. 157(1927), 214-229.