Browsing by Author "Polat, Faruk"

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    Cesaro Vector Lattices and Their Ideals of Finite Elements
    (Springer, 2023) GÖNÜLLÜ, UĞUR; Polat, Faruk; Weber, Martin R. R.
    For the Cesaro matrix C = (c(nm))(n,m?N), where c(nm) = (1)/(n), if n = m and c(nm) = 0 otherwise, the Cesaro sequence spaces ces(0), ces(p) (for 1 < p < 8) and cesoo are defined. These spaces turn out to be real vector lattices and with respect to a corresponding (naturally introduced) norm they are all Banach lattices, and so possess (or not possess) some interesting properties. In particular, the relations to their generating ideals c(0), t(p) and t(8) are investigated. Finally the ideals of all finite, totally finite and selfmajorizing elements in ces(0), ces(p) (for 1 < p <8) and ces(8) are described in detail.
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    Duals of Cesaro Sequence Vector Lattices, Cesaro Sums of Banach Lattices, and Their Finite Elements
    (Springer Basel AG, 2023) GÖNÜLLÜ, UĞUR; Polat, Faruk; Weber, Martin R.
    In this paper, we study the ideals of finite elements in special vector lattices of real sequences, first in the duals of Cesaro sequence spaces ces(p) for p is an element of{0}boolean OR[1,infinity) and, second, after the Cesaro sum ces(p)(X) of a sequence of Banach spaces is introduced, where p = infinity is also allowed, we characterize their duals and the finite elements in these sums if the summed up spaces are Banach lattices. This is done by means of a remarkable extension of the corresponding result for direct sums.
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    Generalized Alexandroff Duplicates and CD 0(K) spaces
    (2006) Çağlar, Mert; Ercan, Zafer; Polat, Faruk; ÇAĞLAR, MERT; 108339; 181147; 1949
    We define and investigateCD Σ,Γ(K, E)-type spaces, which generalizeCD 0-type Banach lattices introduced in [1]. We state that the space CD Σ,Γ(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8].