Gene M. Tucker provides an explanation of Isaiah authorship in The New Interpreter's Bible commentary.
Gene M. Tucker, "Isaiah 1-39 Introduction," The New Interpreter's Bible, 10 vols. (Abingdon Press: Nashville, TN, 2001) 6: 32-35
There were two particularly troubling aspects of this sources-critical investigation of the prophets. First, although many readers of the prophetic books were disturbed by conclusions that such and such a passage did not originate with the prophet in question, even more misleading was the implication that one could, through such analysis, arrive at the authentic words of the prophet. Second, decisions concerning authorship or origin often entailed judgments about the relative value or validity of particular texts. Just as tradition valued the entire books as words of an inspired prophet, so also critics considered the "authentic" words of the prophet more valuable than those of the later editors. But it is only on the basis of a particular understanding of inspiration that the speeches of Isaiah of Jerusalem can be regarded as more theologically authoritative than later additions to the tradition. One is entitled to value judgments, but they should not be confused with judgments of fact concerning origin (see the Reflections at Isa 4:2-6).
Nevertheless, the questions posed by such analysis remain key interpretive steps in the study of prophetic texts. Introductory and concluding formula enable the reader to recognize distinct units within the literature, structures common to particular genres show more clearly what is distinctive about a passage about hot it relates to others, and the concern with social context (setting) helps one to understand how texts functioned in antiquity. Moreover, such questions have proved to productive when applied to entire books as well as to small units of discourse.
The literary pursuit of authorship and the search for the original oral discourse of Isaiah are considered both more difficult and less significant than was the case only a few decades ago. If earlier generations of critical scholarship privileged the oldest, often at the expense of the actual written text, the current tendency is to privilege the latest, or canonical, form of the literature, sometimes at the expense of individual units and their precanonical history. This leads to what should be another rule for biblical interpretation: Throw nothing away. All texts in these chapters and all layers of their development are potentially significant. There is life both in and behind the texts. Nor should one neglect the subsequent life of these texts as they came to echo in later biblical books, including the New Testament. So to read such rich and highly textured literature requires bifocals and more; its depths should not be sacrificed to a focus on one or another of its strata. Finally, if one level or one text is to be considered more valuable or more authoritative than another, that should not be determined on the basis of relative antiquity but on carefully considered theological grounds.
So is it possible to sort out the words of the prophet from words of the book? The best one can do is to establish relative proximity to Isaiah's time and place, and that only when there is sufficient evidence. Such determination, when possible, is important, for it opens the door to deeper understanding. In any case, one needs to be occupied mainly with the text more than with its background, or even the text regardless of its background or origin. The book rather than the prophet Isaiah is what lies before us. Nevertheless, preoccupation with the unity of the entire book should not be allowed to obscure its individual parts or its pre-history.