A formula for the $g$-angle between two subspaces of a normed space

TL;DR

This paper introduces a new concept called the $g$-angle to measure the relationship between subspaces in normed spaces, providing explicit formulas especially for $ ext{l}^p$ spaces, enhancing geometric understanding.

Contribution

It develops the notion of the $g$-angle between subspaces in normed spaces and derives explicit formulas for $ ext{l}^p$ spaces, extending geometric analysis tools.

Findings

Defined the $g$-angle between subspaces in normed spaces.

Derived explicit formulas for the $g$-angle in $ ext{l}^p$ spaces.

Analyzed the $g$-angle between subspaces of various dimensions.

Abstract

We develop the notion of $g$-angle between two subspaces of a normed space. In particular, we discuss the $g$-angle between a $1$-dimensional subspace and a $t$-dimensional subspace for $t\geq 1$ and the $g$-angle between a $2$-dimensional subspace and a $t$-dimensional subspace for $t\geq 2$. Moreover, we present an explicit formula for the $g$-angle between two subspaces of $\ell^{p}$ spaces.