Are there any books besides Abstract Harmonic Analysis by Hewitt and Ross to study $\frak{E}$$_p(I)$?
Where $\frak{E}$$_p(I)$ is: Let $ I $ be an arbitrary index set. For each $i\in I$, let $H_i$ be a finite dimensional Hilbert space of dimension $d_i$, and let $a_i$ be a real number $\geq{1}$. The $\ast$-algebra $\prod_{i\in{I}}\mathcal{B}(H_i)$, will denoted by $\frak{E}$$(I)$. With scalar multiplication, addition, multiplication, and the adjoint of an element are defined coordinatewise, it will be an algebra.
Let $E=(E_i)_{i}$ be an element of $\frak{E}$${(I)}.$ For $p\geq0$, we define $$\|E\|_{p}=\Big( \sum_{i=1}{a_i\|E_i\|}^{p}_{\varphi_p}\Big)^{1/p}$$ and $$\|E\|_{\infty}=\sup\{\|E_i\|_{\varphi_{\infty}},~i\in I\}.$$ For $p\geq0$, $\frak{E}$$_p(I)$ is defined as the set of all $E\in\frak{E}$$_p(I)$ for which $\|E\|_{p}<\infty.$ Hewitt and Ross haves shown that for $1\leq p\leq\infty$, $\frak{E}$$_p(I)$ is a Banach algebra).
Note that for $\|E_i\|_{\varphi_p}=$ $E_i$'s schatten $p$-norm: $o\leq p<\infty$, $$\|E_i\|_{\varphi_p}=\Big(\sum_{j=1}^{n}{|s_{j}^{i}|}^p\Big)^{1/p}$$ and $$\|E_i\|_{\varphi_{\infty}}=\sup\lbrace{s_{1}^{i},s_{2}^{i},...,s_{d_{i}}^{i}}\rbrace,$$ where $(s_{1}^{i},s_{2}^{i},...,s_{d_{i}}^{i})$ is the sequence of eigenvalues of operator $|E_{i}|$, written in any order.