【摘要】 自从 A.N.Serstnev 于1963年提出概率赋范线性空间(记为 M—PN—SP)以来,有许多文章研究了 M—PN—SP 上线性算子的性质。本文在此基础上,考虑 M—PN—SP 的算子的延拓和紧算子;并进一步证明了强有界线性算子和紧线性算子的延拓定理。还证明了有界线性算子空间的完备定理。更多还原

【Abstract】 The concept of compact linear operator on the probabilistic normed spaces is defined in this paper. Moreover,the extention theorem of strong bounded linear operator and compact linear operator,as well as the complete therom of the linear operator space are proved更多还原