Yu-Xia LIANG, Ze-Hua ZHOU

6998

Disjoint supercyclic powers of weighted shifts on weighted sequence spaces

We characterize the disjoint supercyclicity of finitely many different powers of weighted shifts acting on the weighted sequence spaces l2(N,w), c0(N,w) , and l2(Z,w), c0(Z,w), where w=(wi)i is a positive weight sequence satisfying wi \geq 1 for every i\in N (or i\in Z).
Anahtar Kelimeler:

Disjoint supercyclic, unilateral shifts, bilateral shifts, weighted sequence spaces

Disjoint supercyclic powers of weighted shifts on weighted sequence spaces

We characterize the disjoint supercyclicity of finitely many different powers of weighted shifts acting on the weighted sequence spaces l2(N,w), c0(N,w) , and l2(Z,w), c0(Z,w), where w=(wi)i is a positive weight sequence satisfying wi \geq 1 for every i\in N (or i\in Z).
Keywords:

Disjoint supercyclic, unilateral shifts, bilateral shifts, weighted sequence spaces,

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  • limmax  q→∞ i=1 as,i  = limmax  q→∞ aiwnq ∏i=−2nqq i=1ai i=1 ai  = limmax  q→∞ n i=1ai i=1i = 9 4q→∞  ∏2q i=1 ai i=1 ai  = 9 limmax q→∞ 22 q−1, q−1 2 By corollary 4.3 we obtain that the operators Baand B2satisfy the condition (b); thus, they are d-supercyclic. ✷ For p≥ 1, the weighted spaces lp(N, w) and lp(Z, w) are defined by lp(N, w) :=
Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
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