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A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces

S. Grivaux ; Maria Roginskaya (Institutionen för matematiska vetenskaper, matematik)
Proceedings of the London Mathematical Society (0024-6115). Vol. 109 (2014), 3, p. 596-652.
[Artikel, refereegranskad vetenskaplig]

We present a general method for constructing operators without non-trivial invariant closed subsets on a large class of non-reflexive Banach spaces. In particular, our approach unifies and generalizes several constructions due to Read of operators without non-trivial invariant subspaces on the spaces l(1), c(0) or circle plus(l2) J, and without non-trivial invariant subsets on l(1). We also investigate how far our methods can be extended to the Hilbertian setting, and construct an operator on a quasi-reflexive dual Banach space which has no non-trivial w*-closed invariant subspace.

Nyckelord: Banach-Spaces, Reflexitivity, Mathematics



Denna post skapades 2014-11-14. Senast ändrad 2016-07-25.
CPL Pubid: 205819

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur