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The algebra of bounded linear operators\break on ℓp ⊕ ℓp has infinitely many closed ideals

Thomas Schlumprecht EMAIL logo and András Zsák


We prove that in the reflexive range 1<p<q<, the algebra (pq) of all bounded linear operators on pq has infinitely many closed ideals. This solves a problem raised by A. Pietsch [4, Problem 5.3.3] in his book ‘Operator ideals’.

Dedicated to the memory of Ted Odell

Award Identifier / Grant number: DMS-1160633

Funding statement: The first author’s research was supported by NSF grant DMS-1160633. The second author was supported by the 2014 Workshop in Analysis and Probability at Texas A&M University.


We would like to thank the referee for a very careful reading of our paper and for making numerous helpful suggestions to improve it.


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Received: 2014-10-18
Revised: 2015-2-23
Published Online: 2015-6-30
Published in Print: 2018-2-1

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