Operators having no non‐trivial closed invariant subspaces on ℓ1: a step further. Issue 3 (19th September 2018)

• Record Type: Journal Article
• Authors: Gallardo‐Gutiérrez, Eva A.; Read, Charles
• Is Part Of: Proceedings of the London Mathematical Society. Volume 118:Issue 3(2019)
• Page Start: 649
• Page End: 674
• Publication Date: 2018-09-19
• Subjects: 47A15 (primary); Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms.12194
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract: We show the existence of a linear bounded operator T on ℓ 1 such that no polynomial in T has non‐trivial closed invariant subspaces, proving a conjecture by Read [ J. Lond. Math. Soc . 34 (1986) 335–348] posed in 1986 . Moreover, such an operator T is quasinilpotent and satisfies that p ( T ) has no non‐trivial closed invariant subspaces for any non‐constant analytic germ p, strengthening so far the previous known counterexamples in the area.