A Note on $g$-Angle between Two Subspaces in a Normed Space

TL;DR

This paper introduces a new 2-norm based on a semi-inner product to define and revise the formula for the g-angle between 2-dimensional subspaces in a normed space.

Contribution

It proposes a novel 2-norm and a revised formula for the g-angle between subspaces, improving upon previous methods.

Findings

New 2-norm constructed using semi-inner product

Revised formula for g-angle between 2D subspaces

Enhances understanding of angles in normed spaces

Abstract

We introduce a new $2$-norm on a normed space using a semi-inner product $g$ on the space. Using the $2$-norm, we propose a formula for the $g$-angle between $2$-dimensional subspaces in the space. Our formula serves as a revision of the one proposed by Nur {\it et al.} \cite{Nur1}.