Abstract
For every prime numberk, we give an explicit construction of a complexk-dimensional spaceX k with projection constantγ(X k ) = √k − 1/√k + 1/k. Moreover, there are realk-dimensional spacesX k withγ(x K ) ≧ √k − 1 for a subsequence of integersk. Hence in both casesγ(X k )/√k → 1 which is the maximal possible value sinceγ(X k ) ≦ √k is generally true.
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König, H. Spaces with large projection constants. Israel J. Math. 50, 181–188 (1985). https://doi.org/10.1007/BF02761398
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DOI: https://doi.org/10.1007/BF02761398