Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772405 | Journal of Functional Analysis | 2017 | 16 Pages |
Abstract
The GurariÄ space is the unique separable Banach space G which is of almost universal disposition for finite-dimensional Banach spaces, which means that for every ε>0, for all finite-dimensional normed spaces EâF, for every isometric embedding e:EâG there exists an ε-isometric embedding f:FâG such that fâ¾E=e. We show that GN 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 GurariÄ space, recently constructed by GarbuliÅska-WÄgrzyn and the third author. In addition, we consider a non-graded sequence of semi-norms on GN with which the space GN 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 GN is universal in the class of all separable Fréchet spaces.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Christian Bargetz, Jerzy KÄ
kol, WiesÅaw KubiÅ,