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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.

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Is the Lorentz space $L_{W,1}(0,1)$ isomorphic to $L_1(0,1)$?

Let $W$ be a positive non-increasing continuous function on $(0,1]$ so that $\lim_{t \rightarrow 0} W(t)=\infty$, $W(1)=1$ and $\int_0^1 W(t) dt =1$. For $1 \leq p <\infty$, the Lorentz function space …