• Title, Summary, Keyword: representable operators

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THE NEARLY HENSTOCK-STIELTJES REPRESENTABLE OPERATORS

  • Yoon, Ju Han;Park, Jae Myung;Lee, Deok Ho;Kim, Byeong Moo
    • Journal of the Chungcheong Mathematical Society
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    • v.12 no.1
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    • pp.179-186
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    • 1999
  • In this paper, we define the Henstock-Stieltjes representable and nearly Henstock-Stieltjes representable operators for vector-valued function, which are the generalizations of Pettis representable operator and then study some properties of these operators.

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ON THE PETTIS-DIVISOR PROPERTY FOR DUNFORD-PETTIS OPERATORS

  • SUNG-JIN CHO;CHUN KEE PARK
    • Communications of the Korean Mathematical Society
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    • v.13 no.4
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    • pp.775-780
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    • 1998
  • In this paper it is shown that Dunford-Pettis operators obey the "Pettis-divisor property": if T is a Dunford-Pettis operator from $L_1$($\mu$) to a Banach space X, then there is a non-Pettis representable operator S : $L_1$($\mu$)longrightarrow$L_1$($\mu$) such that To S is Pettis representable.

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ON C-STIELTJES INTEGRAL OF BANACH-VALVED FUNCTIONS

  • Zhang, Xiaojie;Zhao, Dafang;Ye, Guoju
    • The Pure and Applied Mathematics
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    • v.14 no.2
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    • pp.71-84
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    • 2007
  • In this paper, we define the C-Stieltjes integral of the functions mapping an interval [a,b] into a Banach space X with respect to g on [a,b], and the C-Stieltjes representable operators for the vector-valued functions which are the generalizations of the Henstock-Stieltjes representable operators. Some properties of the C-Stieltjes operators and the convergence theorems of the C-Stieltjes integral are given.

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THE NEARLY $H_1$-STIELTJES REPRESENTABLE OPERATORS

  • Yoon, Ju-Han
    • The Pure and Applied Mathematics
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    • v.8 no.1
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    • pp.53-59
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    • 2001
  • In this paper, we define the $H_1$-Stieltjes representable, nearly $H_1$-Stieltjes represnetable for vector-valued function, which is the generalization of Bochner representable and than study some properties of these operators.

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