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- Title
Uniqueness of the maximal ideal of operators on the ℓp-sum of ℓ∞n (n ∈ $\mathbb{N}$) for 1 < p < ∞.
- Authors
KANIA, TOMASZ; LAUSTSEN, NIELS JAKOB
- Abstract
A recent result of Leung (Proceedings of the American Mathematical Society, 2015) states that the Banach algebra ℬ(X) of bounded, linear operators on the Banach space X = (⊕n∈$\mathbb{N}$ ℓ∞n)ℓ1 contains a unique maximal ideal. We show that the same conclusion holds true for the Banach spaces X = (⊕n∈$\mathbb{N}$ ℓ∞n)ℓp and X = (⊕n∈$\mathbb{N}$ ℓ1n)ℓp whenever p ∈ (1, ∞).
- Subjects
UNIQUENESS (Mathematics); MAXIMAL ideals; LINEAR operators; BANACH algebras; BANACH spaces
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2016, Vol 160, Issue 3, p413
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004115000766