A separable Frechet space of almost universal disposition

摘要

The Guraxii 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 of F for every isometric embedding e: Epsilon -> G there exists an epsilon-isometric embedding f : F -> G such that f up arrow 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 construetion relies heavily on the universal operator on the Gurarfl space, recently constructed by Garbulinska-Wegrzyn and the third author. In addition, we consider a non-graded sequence of semi-norms on G(N) with which the space G(N) is of almost universal disposition for finite-dimensional Frechet spaces with a fixed sequence of semi-norms. In both cases, this yields in partitular that G(N) is universal in the class of all separable Frechet spaces. (C) 2016 Elsevier Inc. All rights reserved.