Large subspaces ofl
∞
n
and estimates of the gordon-lewis constantand estimates of the gordon-lewis constant |
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Authors: | T Figiel W B Johnson |
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Institution: | (1) Institute of Mathematics, Polish Academy of Sciences, Poland;(2) The Ohio State University, 43210 Columbus, Ohio, USA |
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Abstract: | Lower bounds are obtained for thegl constants and hence also for the unconditional basis constants of subspaces of finite dimensional Banach spaces. Sharp results
are obtained for subspaces ofl
∞
n
, while in the general case thegl constants of “random large” subspaces are related to the distance of “random large” subspaces to Euclidean spaces. In addition,
a new isometric characterization ofl
∞
n
is given, some new information is obtained concerningp-absolutely summing operators, and it is proved that every Banach space of dimensionn contains a subspace whose projection constant is of ordern
1/2.
The research for this paper was begun while both authors were guests of the Mittag-Leffler Institute.
Supported in part by NSF-MCS 79-03042. |
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Keywords: | |
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