In this short note, we prove that for a dense set A⊂ X (X is a Banach space) there is a non-
trivial closed subspace M⊂ X such that A∩ M is dense in M. We use this result to answer a …

A bounded linear operator T on a Banach space X is called subspace-hypercyclic for a
subspace M if Orb (T, x)∩ M is dense in M for a vector x∈ M. We show examples that …

Let G be a second countable locally compact group, B a Borel σ-algebra and let v be a Borel
measurable weight function on G. In this paper, we study the subspace-hypercyclicity of the …

In this paper, we define and study subspace-diskcyclic operators. We show that subspace-
diskcyclicity does not imply diskcyclicity. We establish a subspace-diskcyclic criterion and …

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We apply the well-known and also the newly introduced notions from bounded linear
dynamics to unbounded linear operators. We present a hypermixing criterion similar to that …

A bounded linear operator $ T $ on a Banach space $ X $ is called subspace-hypercyclic for
a nonzero subspace $ M $ if $ orb\left ({T, x}\right)\cap M $ is dense in $ M $ for a vector …

A $ C_ {0} $-semigroup $\mathcal {T}=(T_ {t}) _ {t\geq0} $ on a Banach space $ X $ is called
subspace-supercyclic for a subspace $ M, $ if $\mathbb {C} Orb (\mathcal {T}, x)\bigcap …

Let G be an abelian semigroup of matrices on K n (n≥ 1), K= R or C. We say that G is
subspace-supercyclic for a non-zero subspace M of K n, if there exists x∈ K n such that KG …

In this article, we justify that every separable infinite dimensional complex Banach space
admits an M-hypercyclic C0-semigroups. Also, we prove that if (Tt) t≥ 0 is an M-hypercyclic …