Operators Approximable by Hypercyclic Operators

J. Boland
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Abstract

We show that operators on a separable infinite dimensional Banach space $X$ of the form $I +S$, where $S$ is an operator with dense generalised kernel, must lie in the norm closure of the hypercyclic operators on $X$, in fact in the closure of the mixing operators.
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由超循环算子逼近的算子
我们证明了可分离无限维Banach空间$X$上的算子,其形式为$I +S$,其中$S$是一个具有密集广义核的算子,它必须位于$X$上的超循环算子的范数闭包中,实际上是位于混合算子的闭包中。
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