2-Normed D-Modules and Hahn-Banach Theorem for D-linear 2-functionals
Kulbir Singh, Romesh Kumar
TL;DR
This paper introduces D-valued 2-norms and D-linear 2-functionals on modules, establishing a Hahn-Banach type extension theorem, advancing the theory of D-modules and functional analysis.
Contribution
It defines D-valued 2-norms and D-linear 2-functionals, and proves a Hahn-Banach extension theorem for these functionals, which is a novel development.
Findings
Defined D-valued 2-norms on modules
Introduced D-linear 2-functionals and studied their properties
Proved a Hahn-Banach type extension theorem for D-linear 2-functionals
Abstract
In this paper we introduce the notion of D-valued 2-norm on hy- perbolic or D-valued modules. Further, we define D-linear 2-functional on these modules and consider some of their properties. We also establish the Hahn- Banach type extension theorem for D-linear 2-functionals.
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Taxonomy
TopicsHolomorphic and Operator Theory · Mathematical Analysis and Transform Methods · Algebraic and Geometric Analysis