Dynamics of weighted shifts on directed trees
نویسندگان
چکیده
We study the dynamical behaviour of weighted shifts defined on sequence spaces a directed tree. In particular, we characterize their boundedness as well when they are hypercyclic, weakly mixing and mixing.
منابع مشابه
On Polynomially Bounded Weighted Shifts
(1) ‖p(T )‖ ≤M sup{|p(ζ)| : |ζ| = 1} ∀ polynomial p, and to be power bounded (notation T ∈ (PW)) if (1) holds for every polynomial of the special form p(ζ) = ζ where n is a positive integer. If T ∈ (PB) [resp., T ∈ (PW)], then there is a smallest number M which satisfies (1) [resp., (1) restricted]. This number will be called the polynomial bound of T [resp., the power bound of T ] and denoted ...
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Article history: Received 6 January 2011 Accepted 16 June 2011 Available online 18 July 2011 Submitted by S. Kirkland AMS classification: 05C50 05C05 15A18
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2023
ISSN: ['1943-5258', '0022-2518', '1943-5266']
DOI: https://doi.org/10.1512/iumj.2023.72.9315