Local subspace transitivity criterion

Document Type : Original Article


Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran



An operator ‎$‎T‎$ ‎on‎ Banach space ‎$X‎‎$‎ is called transitive,‎
‎‎i‎f for every nonempty open subsets ‎$‎U‎$‎,‎$‎V$ of $X$‎, ‎there is a positive integer $n‎‎$‎, ‎
‎such that $T^n (U) \cap ‎V ‎‎\neq‎\phi‎‎‎$.
‎In the present paper‎,‎ local subspace transitivite operators are introduced‎.‎
We also provide nontrivial example and establish some basic properties of such operators.
‎Moreover the local subspace transitivity criterion is stated‎.‎ ‎Also,‎ ‎we ‎show ‎‎an operator may
satisfies in the local subspace transitivity criterion without being topological transitive.