＊-伴隨算子

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Title:	＊-伴隨算子
Other Titles:	＊-adjoint of operators
Authors:	詹安茹;Chan, An-ju
Contributors:	淡江大學數學學系碩士班劉豐哲;Liu, Feng-zhe
Keywords:	伴隨算子;自伴隨算子;＊-伴隨算子;＊-自伴隨算子;線性算子;共軛線性算子;賦範向量空間;adjoint operator;self-adjoint operator;＊-adjoint operator;＊-self-adjoint operator;linear operator;conjugate linear operator;normed vector space
Date:	2009
Issue Date:	2010-01-11 02:57:06 (UTC+8)
Abstract:	本論文的對象是由賦範向量空間到賦範向量空間的對偶空間的線性或共軛線性算子，我們稱這種算子為＊-算子。對這種算子，我們定義了它的＊-伴隨算子。＊-伴隨算子的定義域較傳統的伴隨算子的定義域為小，卻因此可引入從一賦範向量空間到它的對偶空間的算子的自伴隨性，大大地擴張了自伴隨性的適用範圍，＊-伴隨算子的引入是參考了希爾伯特空間上伴隨算子的特殊性，目的在縮小它和一般賦範向量空間的算子的伴隨算子的差異性。這篇論文主要的目的是對＊-伴隨算子做初步的討論。 The object in the present paper is a linear operator or a conjugate linear operator, which is defined from a normed vector space into the dual space of a normed vector space. We call it ＊-operator. For this operator, we define its ＊-adjoint operator. The domain of ＊-adjoint operator compares the domain of traditional adjoint operator to be small, but we can introduce the self-adjoint operator defined from a normed vector space into its dual space. This expanded greatly the applicable situation of a self-adjoint operator. ＊-adjoint operator''s introduction has referred to the particularity of adjoint operator in the Hilbert space, and the purpose is to reduce the difference between it and the operator''s adjoint operator of general normed vector space. The present study aims to investigate the initial properties of the ＊-adjoint operator.
Appears in Collections:	[Department of Applied Mathematics and Data Science] Thesis

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