A separable Fréchet space of almost universal disposition

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• 作者：Christian Bargetz^a ; ^b ; ^{bargetz@tx.technion.ac.il} ; Jerzy Kąkol^c ; ^d ; ¹ ; ^{kakol@amu.edu.pl} ; Wiesław Kubiś^d ; ^e ; ² ; ^{kubis@math.cas.cz}
• 关键词：46A61 ; 46A04 ; 46B20 ; 46M40
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：272
• 期：5
• 页码：1876-1891
• 全文大小：347 K
• 卷排序：272

文摘

The Gurariĭ space is the unique separable Banach space GG which is of almost universal disposition for finite-dimensional Banach spaces, which means that for every ε>0ε>0, for all finite-dimensional normed spaces E⊆FE⊆F, for every isometric embedding e:E→Ge:E→G there exists an ε  -isometric embedding f:F→Gf:F→G such that f↾E=ef↾E=e. We show that GNGN with a special sequence of semi-norms is of almost universal disposition for finite-dimensional graded Fréchet spaces. The construction relies heavily on the universal operator on the Gurariĭ space, recently constructed by Garbulińska-Węgrzyn and the third author. In addition, we consider a non-graded sequence of semi-norms on GNGN with which the space GNGN is of almost universal disposition for finite-dimensional Fréchet spaces with a fixed sequence of semi-norms. In both cases, this yields in particular that GNGN is universal in the class of all separable Fréchet spaces.