Operators having no non-trivial closed invariant subspaces on l1: a step further

被引：4
|
作者：
Gallardo-Gutierrez, Eva A. [1 ]
Read, Charles [2 ]
机构：
[1] Univ Complutense Madrid, Fac Matemat, Dept Anal Matemat, Inst Ciencias Matemat ICMAT, Pl Ciencias 3, E-28040 Madrid, Spain
[2] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England
来源：
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2019年 / 118卷 / 03期
关键词：
47A15; (primary);
D O I：
10.1112/plms.12194
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show the existence of a linear bounded operator T on l1 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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页码：649 / 674
页数：26
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