This is an announcement for the paper "A unified construction yielding precisely Hilbert and James sequences spaces" by Dusan Repovs and Pavel V. Semenov.

Abstract: Following James' approach, we shall define the Banach space $J(e)$ for each vector $e=(e_1,e_2,...,e_d) \in \Bbb{R}^d$ with $ e_1 \ne 0$. The construction immediately implies that $J(1)$ coincides with the Hilbert space $i_2$ and that $J(1;-1)$ coincides with the celebrated quasireflexive James space $J$. The results of this paper show that, up to an isomorphism, there are only the following two possibilities: (i) either $J(e)$ is isomorphic to $l_2$ ,if $e_1+e_2+...+e_d\ne 0$ (ii) or $J(e)$ is isomorphic to $J$. Such a dichotomy also holds for every separable Orlicz sequence space $l_M$.

Archive classification: math.GN math.FA

Mathematics Subject Classification: 54C60; 54C65; 41A65; 54C55; 54C20

The source file(s), ArchiveVersion.tex: 21648 bytes, is(are) stored in gzipped form as 0804.3131.gz with size 8kb. The corresponding postcript file has gzipped size 65kb.

Submitted from: dusan.repovs@guest.arnes.si

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