Abstract:It has been established that a $DF$-space having a fully-$\lambda(P)$-basis is $\lambda(P)$-nuclear wherein $P$ is a stable nuclear power set of infinite type. It is shown that a barrelled $G_1$-space $\lambda(Q)$ is uniformly $\lambda(P)$-nuclear iff $\{e_i,e_i\}$ is a fully-$\lambda(P)$-basis for $\lambda(Q)$. Suppose $\lambda$ is a $\mu$-perfect sequence space for a perfect sequence space $\mu$ such that there exist $u\in \lambda^\mu$ and $v\in \mu^x$ with $u_i\ge \varepsilon >0$ and $v_i\ge \iota >0$… Show more
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