Abstract
We discuss various asymmetry constants of finite-dimensional Banach spaces in a more generalized frame than that of [2], and solve a problem raised in [7] by finding an increasing sequence of Banach spaces whose diagonal asymmetry constants tend to infinity. We investigate the question of whether the projection constant of everyn-dimensional Banach space is strictly less than\(\sqrt n \), and show that this is so whenn=2.
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The research for this paper was partially supported by NSF-GP-34193.
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Gordon, Y. Asymmetry and projection constants of Banach spaces. Israel J. Math. 14, 50–62 (1973). https://doi.org/10.1007/BF02761534
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DOI: https://doi.org/10.1007/BF02761534