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研究生： 吳宛諭
Wu, Wan-Yu
論文名稱： 關於跡類算子上的線性泛函
On the linear functionals of trace class operators
指導教授： 黃明傑
Huang, Min-Jei
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2009
畢業學年度： 97
語文別： 英文
論文頁數： 20
中文關鍵詞： 跡類算子 、線性泛函
外文關鍵詞： trace class, linear functional
相關次數： 點閱：2  下載：0 
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    • Let H be a separable infinite dimensional Hilbert space, and let T_1 be the the family of all trace class operators on H. The purpose of this paper is to establish a number of equivalent conditions which characterize the trace among the bounded linear functionals on T_1.

    Contents 1 Introduction ...................1 2 Preliminaries ..................2 3 Main Results ...................3 4 Concluding Remarks ............18 5 Reference .....................19

    [1] M. Reed and B. Simon, Methods of modern mathematical Physics, I : functional analysis, New York : Academic Press, 1980.
    [2] D. Petz and J. Zemanek, Characterization of the trace, Linear Algebra and its Applications 111:43-52 (1988).
    [3] O.E. Tikhonov, Subadditivity Inequalities in von Neumann Algebras and Characterization of Tracial Functionals, Positivity (2005)9:259-264.
    [4] John B. Conway, A course in functional analysis, Springer-Verlag 1990.
    [5] A.M. Bikchentaev, O.E. Tikhonov, Characterization of the trace by Young's inequality, J. Inequal. Pure Appl. Math.6(2)(2005), article 49.
    [6] T. Sano, T. Yatsu, Characterization of the tracial property via inequalities, J.Inequal. Pure Appl.Math. 1(7)(2006), article 36.
    [7] A.M. Bikchentaev, O.E. Tikhonov, Characterization of the trace by monotonicity inequalities, Linear Algebra and its Applications 422:274-278 (2007).
    [8] Li Bing-Ren, Introduction to operator algebras, Singapore : World Scientific, 1992.

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