Almost isometric copies of 𝑙_{∞} in some Banach spaces

Hudzik, H.; Mastyło, M.

doi:10.1090/S0002-9939-1993-1146861-9

Almost isometric copies of $l_ \infty$ in some Banach spaces
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by H. Hudzik and M. Mastyło PDF

Proc. Amer. Math. Soc. 119 (1993), 209-215 Request permission

Abstract:

It is shown that any $\sigma$-complete Banach lattice, with an order semicontinuous norm containing an isomorphic copy of ${l_\infty }$, contains an almost isometric copy of ${l_\infty }$. It is also proved that any Fenchel-Orlicz space (resp. the subspace of finite elements of any Fenchel-Orlicz space) generated by an Orlicz function not satisfying the suitable ${\Delta _2}$-condition contains an almost isometric copy of ${l_\infty }$ (resp. ${c_0}$).

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