M-ideals of compact operators and Norm attaining operators

2024/02/19 by Manwook Han, Han, Manwook, Sun Kwang Kim +1
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2402.12070

openalex publication_date 2024/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate M-ideals of compact operators and two distinct properties in norm-attaining operator theory related with M-ideals of compact operators called the weak maximizing property and the compact perturbation property. For Banach spaces X and Y, it is previously known that if K(X,Y) is an M-ideal or (X,Y) has the weak maximizing property, then (X,Y) has the adjoint compact perturbation property. We see that their converses are not true, and the condition that K(X,Y) is an M-ideal does not imply the weak maximizing property, nor vice versa. Nevertheless, we see that all of these are closely related to property (M), and as a consequence, we show that if K(ℓ_p,Y) (1

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• Operators ideals and approximation properties
• Geometry of the space of compact operators endowed with the numerical radius norm
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