Is there any Banach space other than l^p satisfies these conditions?

Let $X$ be a Banach space.There exists a biorthogonal system $(x_i, f_i)_{i \in \mathbb{N}},$ where $(x_i)_{i \in \mathbb{N}} \subset X$ and $(f_i)_{i \in \mathbb{N}} \subset X^*$ such that for some $p>1$ the conditions:

(i) $\sum_{i = 1}^\infty |f(x_i)|^p < \infty \ \text{for all} \ f \in X^*$;

(ii) $\sum_{i = 1}^\infty |f_i(x)|^q < \infty \ \text{for all} \ x \in X$;

(iii) $\{f_i : i \in \mathbb{N}\}$ is $w^*$-linearly dense in $X^*,$are satisfied, where $\frac{1}{p}+\frac{1}{q} = 1.$

My question is there any Banach space other than $l^p$ satisfies the previous conditions together.Is there any Banach space can satisfy any of these conditions?Can Theorem of Morell and Retherford help in anything

Theorem of Morell and RetherfordIf $X$ is an infinite dimensional Banach space and $(a_i)_{i \in \mathbb{N}}$ is a sequence of real numbers convergent to zero with $0 < a_i < 1,$ then there is a basic sequence $(x_i)_{i \in \mathbb{N}}$ in $X$ such that $\|x_i\| = a_i$ for all $i$ and $$\displaystyle \sup \Big \{\left (\displaystyle \sum_{i=1}^\infty |x^*(x_i)|^2 \right )^{1/2} : x^* \in X^*, \|x^*\| \leq 1 \Big \} \leq 1.$$