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首页> 外文期刊>Journal of Functional Analysis >LINEAR STRUCTURE OF HYPERCYCLIC VECTORS
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LINEAR STRUCTURE OF HYPERCYCLIC VECTORS

机译：超级向量的线性结构

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A vector x in a Banach space B is called hypercyclic for a bounded linear operator T: B --> B if the orbit {T(n)x: n greater than or equal to 1} is dense in B. Our main result states that if T is a compact perturbation of an operator of norm less than or equal to 1 and satisfies an appropiate extra hypothesis, then there is an infinite-dimensional closed subspace consisting, except for zero, entirely of hypercyclic vectors for T. In particular the result applies to compact perturbations of the identity. We also include applications to some weighted backward shifts and compact perturbations of the identity by weighted backward shifts. This last result in combination with a recent one that states that every Banach space admits an operator with a hypercyclic vector proves that in all Banach space there is an operator T with an infinite-dimensional closed subspace consisting, except For zero, of hypercyclic vectors. The main result also applies to the differentiation operator and the translation operator T: f(z) --> f(z + 1)on certain Hilbert spates consisting of entire functions. (C) 1997 Academic Press. [References: 25]
机译：如果轨道{T（n）x：n大于或等于1}在B中是密集的，则对于有界线性算符T：B-> B，Banach空间B中的向量x被称为超循环。我们的主要结果表明如果T是范数小于或等于1的紧致扰动并且满足适当的额外假设，那么将存在一个无限维的封闭子空间，除了零外，它完全包含T的超循环向量。结果适用于身份的紧凑扰动。我们还包括一些加权后移和加权后移对身份的紧凑扰动的应用。最后的结果与最近的结果相结合，最近的结果表明每个Banach空间都允许一个带有超循环向量的算子证明了，在所有Banach空间中，都有一个带有无穷维封闭子空间的算子T，该子空间除零外还包含超循环向量。主要结果也适用于微分算子和平移算子T：f（z）-> f（z + 1）在由整个函数组成的某些希尔伯特波幅上。 （C）1997学术出版社。 [参考：25]

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