Choquet and Shilov Boundaries, Peak Sets, and Peak Points for Real Banach Function Algebras

Table 1

𝐶(𝑋)	𝐶(𝑋,𝜏)
points of 𝑋	points of 𝑋/𝜏
Ch (𝐴,𝑋)	Ch (𝐴,𝑋,𝜏)
(closed) boundary	𝜏-invariant (closed) boundary
Γ(𝐴,𝑋)	Γ(𝐴,𝑋,𝜏)
Theorem 10	Theorem 12
Ch (𝐴,𝑋)	Ch (𝐴,𝑋,𝜏)
Γ(𝐴,𝑋)	Γ(𝐴,𝑋,𝜏)
Theorem 5	Theorem 7(ii)
Choquet set	𝜏-invariant Choquet set
[1, Lemma 1.1]	Theorem 7(i).