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Weak cluster points of maximizing sequences on Banach spaces satisfying
$\boldsymbol {(M_p)}$
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 23 February 2026, pp. 1-8
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- Article
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Let T be a bounded linear operator on a separable Banach space that satisfies geometric properties similar to those of
$\ell ^p,\, p>1$. 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 coincide with the partition, created by considering the norm-attaining property and if the essential norm equals the norm.
