局部緊緻可換群上巴納赫取值函數空間的乘算子

Multipliers of Banach-valued Function Spaces on LCA Group

劉拯德(Cheng-Te Liu)

指導教授 ： 賴漢卿 ； 李金城

中原大學/理學院/應用數學研究所/博士(2016年)

https://doi.org/10.6840/cycu201600185

摘要

本篇論文共分三部份。第一部份我們對定義在局部緊緻阿貝爾群Ｇ上的各種巴納赫取值的函數空間的乘算子刻劃為函數空間並且建立了L^1 (G,A)至L^1 (G,X)的同態A-模乘算子。第二部份設G_1和G_2是局部緊緻豪斯多夫群，E(G_1)、E(G_2)分別是G_1、G_2上的函數空間，若G_1和G_2是同構，蘊涵E(G_1)、E(G_2)是同構。自然地，一個反問題產生：是否E(G_1) 到 E(G_2)的同構，能否導出G_1、G_2是同構？在本文當中，我們將解A^p (G)-代數，1≤p≤2的反問題。第三部份
對任意隨機空間X和Y，考慮以七項數學元素的二人零和動態遊戲，我們建構含選手I及II的遊戲值函數，採取他們的策略在遵守運動定律遊戲系統下，來執行滿足極大極小恒等式之目標函數。而我的論文結果推廣和改進許多文獻上的定理。

關鍵字

乘算子

並列摘要

This thesis is divided into three parts. This first part is that we characterize the multiplier operators of various Banach-valued function defined locally compact abelian group (LCA) to be function spaces. The homomorphism A-module multipliers of L^1 (G,A) into L^1 (G,X) is established. The second part, ifG_1 and G_2 are locally compact Hausdorff groups, E(G_1) and E(G_2) the function spaces (Banach algebras or Banach spaces ) on G_1 and G_2 respectively. Then it is known that if G_1 and G_2 are isomorphic, implies E(G_1) and E(G_2) are isomorphic. Naturally, an inverse problem arises that whether E(G_1) and E(G_2) an algebraic isomorphism could deduce G_1 and G_2 are isomorphic ? In this part, we would solve the inverse problem for A^p (G)-algebra, 1≤p≤2. The third part, X and Y are any stochastic spaces, we consider a two-person zero-sum dynamic game by the seven mathematic elements. We construct a game-valued function including the expectations for players I and II, taking their strategies to perform an objection function satisfying the minimax identity under the game system obey the law of motion. The results of this thesis make an improvement on recent multiplier theories.

並列關鍵字

multiplier

參考文獻

Soc., 1977.

[3]J.C. Candeal Haro and H.C. Lai., “Multipliers in vector-valued function spaces under convolution”, Acta Math. Hung., 67(3):

175-192, 1995.

[4]G.P. Johnson, “Spaces of functions with values in a Banach algebra”, Trans.

Amer. Math. Soc., 92: 411-429, 1959.