On some properties of hyperstonean spaces

Abstract

This paper is devoted to hyperstonean spaces that are precisely the Stone spaces of measure algebras, or the Stone spaces of the Boolean algebras of L-p-projections of Banach spaces for 1 <= p < infinity, p not equal 2. Several new results that have been achieved recently are discussed. Among these, in our opinion, the most significant one is that which states that any Bochner L-p space is the p-direct sum of Bochner L-p-spaces of perfect regular Borel measures on Stonean spaces for 1 <= p < infinity. Overall, we try to shed some light on the inner structure of these spaces, about which very little is known.