Unilateral weighted shifts on ℓ²

2019/04/08 by Beros, Konstantinos A., Larson, Paul B.
#03E15 #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)

paper · doi:10.48550/arxiv.1904.03782

Abstract

Given a unilateral shift B_w (determined by a bounded sequence w), a sequence x ∈ ℓ² is "hypercyclic" for w iff the forward iterates of x under B_w are dense in ℓ². We show that it is possible to make the set of x ∈ ℓ² which are simultaneously hypercyclic for all w in a fixed W ⊆ ℓ^∞ arbitrarily complicated by choosing W appropriately.

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• Disjoint and Simultaneously Hypercyclic Pseudo-Shifts
• Frequently hypercyclic bilateral shifts
• Subspace-hypercyclic weighted shifts
• Disjoint Hypercyclicity along filters
• Disjoint frequently hypercyclic pseudo-shifts