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.

引用

页码：649 / 674

页数：26

共 37 条

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