Browsing by Author "Cengiz, Bahaettin"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    On reflexivity of the Bochner space L-P (mu, E) for arbitrary mu
    (2018) Cengiz, Bahaettin; Gunturk, Banu
    Let (Omega, A, mu) be a finite positive measure space, E a Banach space, and 1 < p < infinity. It is known that the Bochner space L-P (mu, E) is reflexive if and only if E is reflexive. It is also known that L(L-1(mu), E) = L-infinity (mu, E) if and only if E has the Radon-Nikodym property. In this study, as an application of hyperstonean spaces, these results are extended to arbitrary measures by replacing the given measure space by an equivalent perfect one.
  • Thumbnail Image
    Item
    On some properties of hyperstonean spaces
    (2018) Gunturk, Banu; Cengiz, Bahaettin
    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.