An example of 𝑙_{𝑝}-equivalent spaces which are not 𝑙*_{𝑝}-equivalent

Baars, Jan; de Groot, Joost; van Mill, Jan; Pelant, Jan

doi:10.1090/S0002-9939-1993-1184080-0

An example of $l_ p$-equivalent spaces which are not $l^ *_ p$-equivalent
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by Jan Baars, Joost de Groot, Jan van Mill and Jan Pelant PDF

Proc. Amer. Math. Soc. 119 (1993), 963-969 Request permission

Abstract:

We give an example of two locally compact countable metric spaces $X$ and $Y$ which are ${l_p}$-equivalent but not $l_p^{\ast }$-equivalent, i.e., ${C_p}(X)$ and ${C_p}(Y)$ are linearly homeomorphic but $C_p^{\ast }(X)$ and $C_p^{\ast }(Y)$ are not linearly homeomorphic.

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