Introductory books for $\frak{E}$ $_p(I)$ 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,$$‎
‎where $(s_{1}^{i},s_{2}^{i},...,s_{d_{i}}^{i})$ is the sequence of eigenvalues of operator $|E_{i}|$‎, ‎written in any order.
 A: I doubt whether the Banach algebras $\frak{E}$$_p(I)$, where $1 \leq p \leq \infty$, are discussed at other places than $\S 28$ of Abstract Harmonic Analysis by Hewitt & Ross. The reason is that $\frak{E}$$_p(I)$ are considered in $\S 28$ in order to introduce the Fourier transform on compact groups. However, it seems that the setting of $\frak{E}$$_p(I)$ is more general than in fact needed in order to introduce the Fourier transform on compact groups. For example, the Fourier transform on compact groups is covered in Folland's A First Course in Abstract Harmonic Analysis and Deitmar's Principles of Harmonic Analysis, but $\frak{E}$$_p(I)$ does not really occur in these treatments. Therefore, I think the Banach algebras $\frak{E}$$_p(I)$ are really part of Hewitt & Ross' approach to the Fourier transform on compact groups and do not occur outside this approach. 
Most of the theory related to $\frak{E}$$_p(I)$ is in Naimark's Normed Algebras and Dixmier's Von Neumann Algebras. I am not aware of any reference that covers exactly the algebras $\frak{E}$$_p(I)$ other than Hewitt & Ross, but it seems Von Neumann introduced some related concepts in his paper Some matrix-inequalities and metrization of matric space for the first time.
Is there a special reason why you are interested in a (more) introductory book on $\frak{E}$$_p(I)$? I don't think Abstract Harmonic Analysis is ideal for someone that wants an introduction into harmonic analysis, but the volumes are very self-contained and contain in general full details. Furthermore, all the necessary background material for the treatment of the Banach algebras $\frak{E}$$_p(I)$ is in the appendices.
