Schauder Bases and Operator Theory II: (SI) Schauder Operators

Details Schauder Bases and Operator Theory II: (SI) Schauder Operators Schauder Bases and Operator Theory II: (SI) Schauder Operators

2012-04-07

arxiv.org/abs/1204.1587v1

Mathematics

Functional Analysis

It is the 3rd version of our paper

Scientific paper

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.

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