s-Numbers sequences for homogeneous polynomials

TL;DR

This paper extends the theory of s-numbers from linear operators to homogeneous polynomials between Banach spaces, introducing approximation, Kolmogorov, and Gelfand numbers for these polynomials.

Contribution

It generalizes well-known s-number concepts to homogeneous polynomials, establishing key properties and results in this new setting.

Findings

Introduces s-numbers for homogeneous polynomials

Adapts approximation, Kolmogorov, and Gelfand numbers to polynomials

Derives results analogous to linear and multilinear cases

Abstract

We extend the well known theory of $s$-numbers of linear operators to homogeneous polynomials defined between Banach spaces. Approximation, Kolmogorov and Gelfand numbers of polynomials are introduced and some well-known results of the linear and multilinear settings are obtained for homogeneous polynomials.