[Banach] Abstract of a paper by Geng Tian, Youqing Ji, and Yang Cao

This is an announcement for the paper "Schauder bases and operator theory II: (SI) Schauder operators" by Geng Tian, Youqing Ji, and Yang Cao.

Abstract: In this paper, we will show that for an operator $T$ which is injective and has dense range, there exists an invertible operator $X$ (in fact we can find $U+K$, where $U$ is an unitary operator and $K$ is a compact operator with norm less than a given positive real number) such that $XT$ is strongly irreducible. As its application, strongly irreducible operators always exist in the orbit of Schauder matrices.

Archive classification: math.FA

Mathematics Subject Classification: 47A55, 47A53, 47A16, Secondary 54H20

Remarks: It is the 3rd version of our paper

Submitted from: caoyang@jlu.edu.cn

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1204.1587

or

http://arXiv.org/abs/1204.1587