A solution to the invariant subspace problem on the space \(\ell _ 1\). (English) Zbl 0574.47006

Read, C. J.

Bull. Lond. Math. Soc. 17, 305-317 (1985).

The paper is an addendum to the author’s earlier paper [ibid. 16, 337-401 (1984; Zbl 0566.47003)]. In this note he indicates modifications which yield an operator on the space \(\ell_ 1\) with no proper invariant subspaces. The problem for operators on Hilbert space or reflexive Banach spaces remains open.

Reviewer: R.G.Douglas

MSC:

47A15	Invariant subspaces of linear operators
46A45	Sequence spaces (including Köthe sequence spaces)

Keywords:

invariant subspace problem; operator on the space \(\ell _ 1\) with no proper invariant subspaces

Citations:

Zbl 0566.47003