We prove that in the reflexive range , the algebra of all bounded linear operators on 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
Funding source: National Science Foundation
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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