吴智泉.Hilbert空间中有界线性算子的膨胀[J].数学研究及应用,1981,1(1):125~134
Hilbert空间中有界线性算子的膨胀
Concerning the Dilations of Bounded Operators in Hilbert Space
投稿时间:1980-12-09  
DOI:10.3770/j.issn:1000-341X.1981.01.016
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吴智泉 吉林大学 
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      The concept of dilation of bounded operator in Hilbert space introduced by Sz.-Nagy is useful for the operator researches. The main purpose of this note is to give a necessary and sufficient condition for an operator to be a dilation of a bounded operator A and then to distinguish the dilations of an operator into two kinds, exact and unexact dilations, by means of this condition. When we are only concerned with unitary dilations, the concept of exact dilation being nothing but that of minimal unitary dilation. Most of the other results stated in this note may be well known, but have been stated and proved in a new form.
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