Some isomorphically polyhedral orlicz sequence spaces |
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Authors: | Denny H Leung |
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Institution: | (1) Department of Mathematics, National University of Singapore, 0511 Singapore |
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Abstract: | A Banach space is polyhedral if the unit ball of each of its finite dimensional subspaces is a polyhedron. It is known that
a polyhedral Banach space has a separable dual and isc
0-saturated, i.e., each closed infinite dimensional subspace contains an isomorph ofc
0. In this paper, we show that the Orlicz sequence spaceh
M is isomorphic to a polyhedral Banach space if lim
t→0
M(Kt)/M(t)=∞ for someK<∞. We also construct an Orlicz sequence spaceh
M which isc
0-saturated, but which is not isomorphic to any polyhedral Banach space. This shows that beingc
0-saturated and having a separable dual are not sufficient for a Banach space to be isomorphic to a polyhedral Banach space. |
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Keywords: | |
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