The editor tells us that the author died before the work was in print, and the author requested him to publish it without revealing the authorship. Even if the author had lived the book would have appeared anonymously or under a pseudonym. We may presume that the initials are those of the author's name, when we have choice of entry as if the initials were not given, as

Makers of Hellas, The: the philosophy and
religion of Ancient Greece, by E.E.G.; ed.
by Frank B. Jevons. 1903180

with references from the initials and the Editor as

G., E. E. See Makers of Hellas.
Jevons, Frank B. (Ed.) See Makers of Hellas.

or, more conveniently and just as usefully, with an entry instead of a reference under the initials

G., E. E. The makers of Hellas: the philosophy
and religion of Ancient Greece; ed. by Frank
B. Jevons. 1903180

the reference from the Editor then being changed to

Jevons, Frank B. (Ed.) See G., E. E.

or, under the circumstances, an entry might be given