| 概率赋范空间上的有界线性算子与全连续算子 |
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| 引用本文： | 屈瑞斌,林熙.概率赋范空间上的有界线性算子与全连续算子[J].西安交通大学学报,1987(1). |
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| 作者姓名： | 屈瑞斌 林熙 |
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| 作者单位： | 西安交通大学数学系
(屈瑞斌)，西安交通大学数学系(林熙) |
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| 摘 要： | 本文定义了概率赋范线性空间(简称PN 空间)上的全连续算子,并研究了PN空间上强有界线性算子和全连续算子的性质,特别是强有界线性算子空间和全连续算子空间的完备性.文中还给出例子说明PN 空间与通常赋范空间中算子性质的差异.最后,对PN 空间强有界线性算子的逆算子进行了研究.
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| 关 键 词： | 概率赋范线性空间 |
BOUNDED LINEAR OPERATORS AND ABSOLUTE CONTINUOUS OPERATORS IN PROBABILISTIC NORMED LINEAR SPACES |
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| Qu Ruibin Lin Xi.BOUNDED LINEAR OPERATORS AND ABSOLUTE CONTINUOUS OPERATORS IN PROBABILISTIC NORMED LINEAR SPACES[J].Journal of Xi'an Jiaotong University,1987(1). |
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| Authors: | Qu Ruibin Lin Xi |
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| Institution: | Department of Mathematics |
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| Abstract: | This paper gives the definition of absolute continuous operators in proba-
bilistic normed spaces(briefly,PN spaces)and studies the properties of both
bounded linear operators and absolute continuous operators in PN spaces,espe-
cially the sufficient conditions for the completeness of the bounded linear
operator space and the absolute continuous operator space.Several examples are
given in order to show the differences between the PN space and ordinary
linear operator space.Finally,the paper also studies the inverse of bounded
linear operators in PN spaces. |
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| Keywords: | probabilistic normed linear space |
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