Diameter two properties in some vector-valued function spaces

We introduce a vector-valued version of uniform algebra, called the function space over algebra. The diameter two properties algebra on an infinite compact Hausdorff are investigated. Every nonempty relatively weakly open subset unit ball $$A(K, (X, \tau ))$$ dimensional has two, where $$\tau $$ is locally convex topology Banach X compatible to dual pair. Under assumption equipped with norm being uniformly and additional condition that $$A\otimes X\subset A(K, X)$$ , it shown Daugavet points $$\Delta -points X) A same, they characterized by norm-attainment at limit point Shilov boundary A. In addition, sufficient for diametral local property also provided. Similar results hold