Hahn-Banach theorem for operators on the lattice normed f-algebras

2020/01/14 by Abdullah Aydın, Aydın, Abdullah
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2001.04714

openalex publication_date 2020/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X and E be f-algebras and p:X → E₊ be a monotone vector norm. Then the triple (X,p,E) is called a lattice-normed f-algebraic space. In this paper, we show a generalization of the extension of the Hahn-Banach theorem for operators on the lattice-normed f-algebras, in which the extension of one step of that is not similar to the other Hahn-Banach theorems. Also, we give some applications and results.

Related

• Hahn-Banach operators
• Algebras of Lebesgue and KB regular operators in Banach lattices
• Extension of order bounded operators
• Hahn-Banach theorems for κ-normed spaces
• Operators Affiliated to Banach Lattice Properties and the Enveloping Norms