Abstract of a paper by C. Bargetz, J. Kakol and W. Kubis
This is an announcement for the paper “A separable Frechet space of almost universal disposition” by C. Bargetz, J. Kakol and W. Kubis. Abstract: The Gurarii space is the unique separable Banach space $G$ which is of almost universal disposition for finite-dimensional Banach spaces, which means that for every $\epsilon>0$, for all finite-dimensional normed spaces $E\subset F$, for every isometric embedding $e: E\rightarrow G$ there exists an $\epsilon$-isometric embedding $f: F\rightarrow G$ such that $f|E=e$. We show that $G^N$ with a special sequence of semi-norms is of almost universal disposition for finite-dimensional graded Frechet spaces. The construction relies heavily on the universal operator on the Gurarii space, recently constructed by Garbulinska-Wegrzyn and the third author. This yields in particular that $G^N$ is universal in the class of all separable Frechet spaces. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.06361
participants (1)
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Bentuo Zheng (bzheng)