How to understand the notation $(\Sigma \oplus l_{p_k})_2$?

Question

In the book "Geometric Nonlinear Functional Analysis" by Benyamini and Lindenstrauss I came across the following example:

Example Let $E=(\Sigma \oplus l_{p_k})_2$. If $p_k\to \infty$, then the unit closed ball of $E$ is not an absolute neighbourhood uniform retract.

I would like to understand the example, but fail to understand even the symbol $(\Sigma \oplus l_{p_k})_2$ itself.

Could anyone please kindly explain what the space $E$ is?

Answer 1

$E=\{(x_k)_{k\in\mathbb N}\in \prod\limits_{k\in\mathbb N} \ell_{p_k}: \sum\limits_{k\in\mathbb N} \|x_k\|_{p_k}^2<\infty\}$.