An additivity formula for the strict global dimension of C(Ω)

Let A be a unital strict Banach algebra, and let K+ be the one-point compactification of a discrete topological space K. Denote by Open image in new window the weak tensor product of the algebra A and C(K+), the algebra of continuous functions on K+. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension Open image in new window is equal to Open image in new window .