文档介绍：佗一赋范空间的行列式构造$口Minkowski构造摘要以阎革兴的论文(n-赋范空问》和余健波的论文《n—》为基础,我们对n一赋范空间做了如下基本的研究:首先我们对n一赋范空间的具体构造作了初步探讨,不仅赋范空间的范数可以诱导一个n一范数’内积也可生成礼一范数,,可以给定一个满足对称性、‘偏绝对凸性、相容性和吸收性的归零集合A,此时A就可生成一个Minkowski泛函,我们称之为由A生成的n一半范数,:赋范空间X的对偶空间的范数诱导的n一范数和x的对偶n一范数是同一个n一范数;内积空间中由内积诱导的n一范数和由此内积给出的范数诱导的礼一范数也是同一个仡~范数;对于更一般的线性空间x而言,,得到了任何有限维的n一赋范空间都是佗一Banach空间,给出了礼一赋范空间成为n—Bonoch空间的两个特征刻画,并得到了一个“n一范数和范数”比较定理. 关键词:n一范数;Minkowski泛函;相容性;"一Banach空间 THE DETERMINANT CoNSTRUCTIoN AND MINKOWSKI CoNSTRUCTIoN oF n_NORMED LINEAR SPACE AB STRACT Based ontheses{n-normed Space))of Yan Gexing and《n-Banach Space and smooth- ne88 of2-normed space))of Yu Jianbo,we get somepreliminary study about n-normed space asfollows:First,we make somepreliminary study on thespecific construction ofn-normed n-norm not onlyCan beinduced by thenorm of anormed space,but alsoCan bepro- duced by ainner- speaking,a n-norm can alsobeinduced by aHamel basis of ,we can give asetA which satisfiesthesymmetry,partially absolute convex patible property andabsorbing property trending to zero property in theproduct space X“.Thus A can generate theMinkowski functional,which Can becalled then-seminorm generated by we proved that then-semiform generated by es an-norm ifand only ifA ,we alsoget threefundamen- talresults,suchas then-norm inducedby thenorm ofthedualspace of anormedspace Xand the dualn-norm ofX are the same;the n-norm induced by theinner-product of a inner-product space isthe saJne as then-norm induced by thenorm which isinduced by the inner-product;for amore general linearspace X,the n-norm induced by aHamel basisH is thesame as then-norm induced by thenorm generated by ,we make some investigation upon the aspect oftopology inthen-normed space,get aconclusion such as any finitedimen