Strictly singular non-compact operators between L_p spaces

2020/01/27 by Francisco L. Hernández, Hernández, Francisco L., E. M. Semenov +3
Mathematics · #28A78 #46E30 #47B07 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2001.09677

openalex publication_date 2020/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the structure of strictly singular non-compact operators between L_p spaces. Answering a question raised in [Adv. Math. 316 (2017), 667-690], it is shown that there exist operators T, for which the set of points (\frac1p,\frac1q)∈(0,1)× (0,1) such that T:L_p→ L_q is strictly singular but not compact contains a line segment in the triangle \(\frac1p,\frac1q):1

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