Mappings of continuous functions on hyper-Stonean spaces
Let C(K) denote the Banach algebra of continuous real functions, with the supremum norm, on a compact Hausdorff space K. For two subsets of C(K), one can define their product by pointwise multiplication, just as the Minkowski sum of the sets is defined by pointwise addition. Our main interest is in correlations between properties of the product of closed order intervals in C(K) and properties of the underlying space K. When K is finite, the product of two intervals in C(K) is always an interval....
The authors obtain some multiplier theorems on spaces analogous to the classical multiplier theorems of de Leeuw. The main result is that a multiplier operator