Uniqueness of the maximal ideal of operators on the ℓ p -sum of ℓ∞ n (n ∈ N ) for 1 < p< ∞

Kania, Tomasz and Laustsen, Niels (2016) Uniqueness of the maximal ideal of operators on the ℓ p -sum of ℓ∞ n (n ∈ N ) for 1 < p< ∞. Mathematical Proceedings of the Cambridge Philosophical Society, 160 (3). pp. 413-421. ISSN 0305-0041

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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 which is the l1-direct sum of l∞n for n=1,2,... contains a unique maximal ideal. We show that the same conclusion holds true for the Banach space X which is the lp-direct sum of l∞n for n=1,2,...  and its dual space X* whenever 1<p<∞.