Abstract of a paper by Dusan Repovs and Pavel V. Semenov
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3131 or http://arXiv.org/abs/0804.3131 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3131 or in gzipped form by using subject line get 0804.3131 to: math@arXiv.org.
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alspach@fourier.math.okstate.edu