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arXiv · 2508.11420

Weak cluster points of maximizing sequences on Banach spaces satisfying $\boldsymbol{(M_p)}$

David Norrbo
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Abstract

Given a bounded linear operator $T$ on a separable Banach space with property $(M_p)$, we prove that the smallest and the largest norm of weak cluster points of all maximizing sequences for $T$ can only take the values $0$ or $1$. The three classes of bounded linear operators emerging from the dichotomy of these extremal norm values coincides with the partition, created by considering the norm-attaining property and if the essential norm equals the norm.

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David Norrbo. 2025-08-15. Weak cluster points of maximizing sequences on Banach spaces satisfying $\boldsymbol{(M_p)}$. https://doi.org/10.4153/s0008439526101842

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