Interpolation and extrapolation of strictly singular operators between L_p spaces

2017/06/27 by Francisco L. Hernández, Hernández, Francisco L., E. M. Semenov +3
Mathematics · #46B70 #47B07 #47B38 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1706.08682

openalex publication_date 2017/06/27 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study the interpolation and extrapolation properties of strictly singular operators between different L_p spaces. To this end, the structure of strictly singular non-compact operators between L_p-L_q spaces is analyzed. Among other things, we clarify the relation between strict singularity and the L-characteristic set of an operator. In particular, Krasnoselskii's interpolation theorem for compact operators is extended to the class of strictly singular operators.

Related

• Strictly singular non-compact operators between L_p spaces
• Quantifications of strictly singular operators and strictly cosingular operators
• Narrow and ℓ₂-strictly singular operators from L_p
• General Theorem on Interpolation of Compact Operators
• Classes of strictly singular operators and their products