Finite elements in some spaces of operators
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Özet (EN)
The main result of this thesis asserts that all lattice norm 𝗌 𝗍𝗁𝖺𝗍 make a vector lattice into a Banach lattice 𝖺𝗋𝖾 equivalent. Also, for any D𝖾𝖽𝖾𝗄𝗂𝗇𝖽 complete Banach latt 𝕏, then φ1(ℒr(𝕏)) = ℒr(𝕏) if and only if 𝑑𝑖𝑚𝕏 < ∞. Let 𝕏 and 𝕐 be two Banach lattices and 𝕏 be an 𝐴𝐿 - space, 𝕐 D𝖾𝖽𝖾𝗄𝗂𝗇𝖽 complete with an 𝗈𝗋𝖽𝖾𝗋 unit. If 𝜑1(ℒ𝑟(𝕏, 𝕐)) = ℒ𝑟(𝕏, 𝕐), then 𝕏 is lattice isomorphic 𝗍𝗈 an 𝐴𝐿-space and 𝕐 is lattice isomorphic to an 𝐴𝑀-space. Under the same assertions ℒ𝑟(𝕏, 𝕐) has a rank one operator as an 𝚘rd𝚎r unit. If for any 𝒽 ∈ 𝜑1(𝕏′) and for any 𝑦 ∈ 𝕐, the rank one operator𝒽 ⊗ 𝑦 is a 𝖿𝗂𝗇𝗂𝗍𝖾 element in 𝒦(𝕏, 𝕐). 2023, 44 pages Keywords: ordered vector space, Archimedean ordered vector space, Selfmajorizing element, Lattic ısomorphism, F𝗂𝗇𝗂𝗍𝖾 element
Yazar
Maha Alaa Husseın Husseın
Bu Yayına Nasıl Atıf Yapılır
Maha Alaa Husseın Husseın (Master Thesis). Finite elements in some spaces of operators, 2023, Çankırı Karatekin Üniversitesi.
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