The skew generalized von Neumann-Jordan type constant in Banach spaces
Abstract
Recently, the von Neumann-Jordan type constants C(X) has defined by Takahashi. A new skew generalized constant Cp(λ,μ,X) based on C(X) constant is given in this paper. First, we will obtain some basic properties of this new constant. Moreover, some relations between this new constant and other constants are investigated. Specially, with the Banach-Mazur distance, we use this new constant to study isomorphic Banach spaces. Ultimately, by leveraging the connection between the newly introduced constant and the weak orthogonality coefficient ω(X), a sufficient condition for normal structure is established.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.