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研究生： 林淑惠
Sue-Hwi Lin
論文名稱： 關於巴氏空間上連續函數的近乎收斂性
On almost convergence of continuous functions in Banach spaces
指導教授： 高華隆
Hwa-Long Gau
蕭勝彥
Sen-Yen Shaw
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 93
語文別： 中文
論文頁數： 22
中文關鍵詞： 近乎收斂 、巴氏空間
外文關鍵詞： almost convergence, strong almost convergence
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    • 這篇論文主要在研究所有值域在巴氏空間上的連續函數的近乎收斂性、強近乎收斂性、以及(C,1)收斂、C-all*收斂，得到一些新的結果。

    This thesis is concerned with the relations between almost convergence, strongly almost convergence, convergence in (C,1) sense, convergence in C-all* sense in the space C([0,∞), X ) of all continuous function with values in Banach space X. Some counterexamples of these properties are discussed.

    Section 1. Introduction…………………...1 Section 2. Equivalence condition for almost convergence ………………....5 Section 3. Cauchy criterions for almost convergence and strong almost convergence………………….9 Section 4. Tauberian theorem for almost convergence………………...14 Section 5. Tauberian condition from (C,1) convergence to almost convergence………………...16 Section 6. Tauberian condition from C-all* convergence to norm convergenve………………...20 References……………………………………22

    P. L. Butzer and R. J. Nessel,Fourier Analysis and
    Approximation,Vol. 1: one-dimensional theory. Academic Press, New York-London,1971.
    P. L. Butzer and R. J. Nessel,Aspects of de La Vallee-Poussin''s work in approximation and　its influence, Arch. Hist. Exact Sci.46(1993), no. 1,
    67-95.
    Meng-Kuang Kuo, Characterization of w-almost convergent double
    sequences and their related properties, Ph.D. Dissertation, National
    Tsing Hua University, 2004.
    G. G. Lorentz, A contribution to the theory of divergent sequences,　Acta Math.80(1948), 167-190.
    I. J. Maddox, A new type of convergence, Math. Proc. Cambridge-Philos.
    Soc.83(1978), no. 1, 61-64.
    I. J. Maddox, Some general Tauberian theorems,J. London Math.Soc.(2)7(1974), 645-650.

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