Gelfand Triples / Rigged Hilbert Spaces - Reflexivity necessary?

Consider the triple $V=l^1$, $H=l^2$, $V^*=l^\infty$. However, the closure of $l^2$ with respect to the $l^\infty$-norm is $c_0$, which is a closed and proper subspace of $l^\infty$. Hence, the embedding $i^*$ fails to have dense image. This proves that there is some non-reflexive $V$, where the claim fails.

Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$

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Nice parameterization of linear complex structures on the real plane?

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