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Operators having no non‐trivial closed invariant subspaces on ℓ 1 : a step further
Author(s) -
GallardoGutiérrez Eva A.,
Read Charles
Publication year - 2019
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12194
Subject(s) - mathematics , linear subspace , invariant (physics) , reflexive operator algebra , pure mathematics , algebra over a field , computer science , mathematical physics , extension (predicate logic) , compact operator , programming language
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.
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