First, the grammar for CTL* (Figure 4) is correct! I erroneously asked
you to correct it. For example, consider the semantics for the path
formula X g.

M,pi satisfies X g iff pi^1 satisfies g, where pi^1 is the
suffix of pi starting at the first state. So we are interpreting
g as a path formula. 

You should revisit the semantics of U and F in this light!

Now let us revisit the CTL* property AGFp. Let M be a model and s_0
be the initial state of the system. Suppose AGFp is true in s_0. This
means that for every path starting from the state s_0 the "path
formula" GFp is true. Consider a path pi starting from the state
s_0. On every state of the path pi Fp is true. This means that that p
is true infinitely often on path pi (can you reason about this?).  So
AGF p is true in a model M iff on every path starting from the initial
state property p is true infinitely often.

Therefore, the LTL formula AGFp is equivalent to the CTL formula
AGAFp. Hence, we found one more example of an LTL formula that is
equivalent to a CTL formula.