Strict s-numbers of the Volterra operator

TL;DR

This paper computes exact s-numbers for the Volterra operator and related summation operator, providing precise quantitative measures of their compactness and approximation properties.

Contribution

It presents the exact values of various s-numbers for the Volterra operator and the summation operator, advancing the understanding of their operator-theoretic characteristics.

Findings

Exact values of Approximation, Gelfand, Kolmogorov, Mityagin, and Isomorphism numbers for the Volterra operator.

Exact values of the same s-numbers for the summation operator.

Enhanced understanding of the compactness and approximation properties of these operators.

Abstract

For Volterra operator $V\colon L^1(0,1) \to C[0,1]$ and summation operator $\sigma\colon \ell^1 \to c$, we obtain exact values of Approximation, Gelfand, Kolmogorov, Mityagin and Isomorphism numbers.