A general approach to Read%26apos;s type constructions of operators without non-trivial invariant closed subspaces

作者：Grivaux Sophie^*; Roginskaya Maria

来源：Proceedings of the London Mathematical Society, 2014, 109(3): 596-652.

DOI：10.1112/plms/pdu012

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.

• 出版日期2014-9