A characterization of the dual of the classical Lorentz sequence space $d(w,q)$

Abstract:

A new proof is given that regularity of $w$ implies that the dual of the classical Lorentz sequence space $d(w,q)$ is the nonclassical $d({w^{ - q’/q}},q’)$, where $1/q + 1/q’ = 1$. It is also shown that regularity is necessary for this equality to hold.