樊丽颖 张佳宁 曹丽萍 宋婧婧
摘 要:为了研究Banach空间算子的一些几何性质,给出了β算子和弱β算子的定义;讨论了β算子和弱β算子的性质,进一步得到了算子具有β性质的充分必要条件、β算子与具有β性质的空间之间的关系,研究了β算子空间的定义及此空间的性质,得到了β算子是紧算子的判别条件,给出了自反空间一个新的特征。
关键词:β算子;自反空间;弱β算子;β算子空间
DOI:10.15938/j.jhust.2018.02.025
中图分类号: O177.7
文献标志码: A
文章编号: 1007-2683(2018)02-0140-04
Abstract:To study some geometric properties of Banach space operator, the definitions of the β-operator and weak β-operator were given, and the properties of the β-operator and weak β-operator were discussed. Sufficient and necessary conditions for the operator with β-property were obtained. The relationship between properties of β-operator and the space which has β-property were discussed. The definition of β-operator space and the property of this space were studied. The conclusion was obtained that β-operator is a compact operator, and a new feature of reflexive space was given.
Keywords:β-operator; reflexive space; weak β-operator; β-operator space
0 引 言
众所周知,对定义在Banach空间而取值于另一Banach空间的有界线性算子[1-7],其变域的结构在算子结构的研究中起主要作用,文[1]引入了NUC算子以及UKK算子,并对它的性质进行了讨论,得到了NUC算子是UKK的、算子是NUC的充要条件、算子T是NUC算子,则算子T*是NUS算子等结论,作者将定义β算子和弱β算子,这类算子与具有β性质的空间以及弱β性质的空间有密切的关系,证明自反空间β算子为弱β算子等结论。
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