GÖNÜLLÜ, UĞURPolat, FarukWeber, Martin R. R.2023-10-102023-10-102023Gönüllü, U., Polat, F. & Weber, M.R. Cesàro vector lattices and their ideals of finite elements. Positivity 27, (2), (2023).1385-1292https://doi.org/10.1007/s11117-023-00977-7https://hdl.handle.net/11413/8814For 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.eninfo:eu-repo/semantics/restrictedAccessCesaro Sequence SpacesVector LatticeBanach LatticeFinite Elements in Vector LatticesArticle0009533179000012-s2.0-85150688958