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Principal Measure and Uniform Distributional Chaos of Weighted Shift Operators on Σ(X)
LU Tianxiu, ZHU Peiyong, WU Xinxing
Acta Mathematicae Applicatae Sinica ›› 2015, Vol. 38 ›› Issue (1) : 1-7.
PDF(293 KB)
PDF(293 KB)
Principal Measure and Uniform Distributional Chaos of Weighted Shift Operators on Σ(X)
Assume that X is a normed linear space (not necessarily complete) and Σ(X)=XN0. In this paper, it is proved that for weighted shift operator Bw: Σ(X)→Σ(X), (x0, x1, …)→(w0x1, w1x2, …) Bw is distributionally ε-chaotic for any 0<ε X)=2 and the principal measure of Bw is 1. Besides, this property is preserved under iterations.
Weighted shift operator / uniform distributional chaos / principal measure {{custom_keyword}} /
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