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Uniqueness of the maximal ideal of operators on the ℓp-sum of ℓ∞n (n ∈ $\mathbb{N}$) for 1 < p < ∞

Published online by Cambridge University Press:  18 January 2016

TOMASZ KANIA  and
NIELS JAKOB LAUSTSEN
TOMASZ KANIA
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland. e-mail: tomasz.marcin.kania@gmail.com
NIELS JAKOB LAUSTSEN
Affiliation:
Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF. e-mail: n.laustsen@lancaster.ac.uk
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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 = (⊕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, ∞).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 160 , Issue 3 , May 2016 , pp. 413 - 421
Copyright
Copyright © Cambridge Philosophical Society 2016 

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