On some properties of hyperstonean spaces

Authors: BANU GÜNTÜRK, BAHAETTİN CENGİZ

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 $1$ $\leq p<$ $\infty ,$ $% p\neq $ $2.$ 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 $1$ $\leq p<$ $\infty .$ Overall, we try to shed some light on the inner structure of these spaces, about which very little is known.

Keywords: Stonean space, perfect measure, equivalent measures, Bochner space, $p$-direct sum

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