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題 名 | Products of Unipotent Operators of Index 2=指標2冪單算子的乘積 |
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作 者 | 王進賢; | 書刊名 | 海軍軍官學校學報 |
卷 期 | 3 1993.12[民82.12] |
頁 次 | 頁1-6 |
分類號 | 314.72 |
關鍵詞 | 指標2; 乘積; 冪單算子; |
語 文 | 英文(English) |
中文摘要 | 前不久,吳培元教授和作者獲得有限矩陣可表為兩個指標2冪單矩陣乘積的特徵型 式。想推廣該結果到無窮維希伯特空間上的算子似乎是挺困難的事。本論文中,我們開啟了 這方面的研究。主要結果有:(1)證明若算子T是兩指標2冪單算子的乘積則T和T□的譜相 同;(2)獲得正規算子可表為兩個指標2算子乘積的特徵型式。並且利用(1)的結果刻劃 出正規算子可表為四個指標2冪單算子乘積的充要條件。 |
英文摘要 | In a recent work, Pei Yuan Wu and the author obtained a complete characterization of those finite matrices which can be expressed as the product of two unipotent matrices of index 2. Extending this result to operators on a possibly infinite-dimensional Hilbert space seems more difficult. In this paper, we initiate its study and obtain, among other things, that (1) if T is the product of two unipotents of index 2, then the spectra and the essential spectra of T and T□ are the same, and (2) a characterization of products of two unipotents of index 2 among normal operators. Also, using (1), we are able to characterize normal operators which are the product of four unipotents of index 2. *This paper is adapted from the author's doctoral dissertation submitted to National Chiao Tung University in the summer of 1991. The autor wishes to express his sincere gratitiude to Professor Pei Yuan Wu for his guidance and encouragement during the preparation of this paper. |
本系統中英文摘要資訊取自各篇刊載內容。