On the norm of the canonical projection of 𝐸*** onto 𝐸^{⊥}

Johnson, Jerry; Wolfe, John

doi:10.1090/S0002-9939-1979-0529211-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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On the norm of the canonical projection of $E^{\ast \ast \ast }$ onto $E^{\perp }$
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by Jerry Johnson and John Wolfe

Proc. Amer. Math. Soc. 75 (1979), 50-52

DOI: https://doi.org/10.1090/S0002-9939-1979-0529211-0

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Abstract:

For each number t with $1 < t \leqslant 2$, a renorming of ${c_0}$ is given for which $\left \| {I - P} \right \| = t$, where P is the canonical projection of $c_0^{ \ast \ast \ast }$ on $c_0^\ast$.

References

A. L. Brown, On the canonical projection of the third dual of a Banach space onto the first dual, Bull. Austral. Math. Soc. 15 (1976), no. 3, 351–354. MR 430744, DOI 10.1017/S0004972700022784
Y. Benyamini, Near isometries in the class of $L^{1}$-preduals, Israel J. Math. 20 (1975), no. 3-4, 275–281. MR 377571, DOI 10.1007/BF02760332