Abstract
In this paper, we introduce subspace hypercyclicity and transitivity of tuples of operators and we give some relations between these concepts and the subspace transitivity criterion for a tuple of operators. AMS Subject Classification: 47B37, 47B33
Highlights
By an n-tuple of operators we mean a finite sequence of length n of commuting continuous linear operators on a Banach space X.Definition 1.1
Let T = (T1, T2, ..., Tn) be an n-tuple of operators acting on a separable infinite dimensional Banach space X over C and let M be a nonzero subspace of X
Note that if T1, T2, ..., Tn are commutative bounded linear operators on a Banach space X, and {mj(i)}j, is a sequence of natural numbers for i = 1, ..., n, we say {T1mj(1)T2mj(2)...Tnmj(n) : j ≥ 0} is M -hypercyclic if there exists x ∈ X such that {T1mj(1)T2mj(2)...Tnmj(n)x : j ≥ 0} ∩ M is dense in M
Summary
By an n-tuple of operators we mean a finite sequence of length n of commuting continuous linear operators on a Banach space X.Definition 1.1. Let T = (T1, T2, ..., Tn) be an n-tuple of operators acting on a separable infinite dimensional Banach space X over C and let M be a nonzero subspace of X.
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