%0 Journal Article %T Local subspace transitivity criterion %J Khayyam Journal of Mathematics %I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures) %Z 2423-4788 %A Asadipour, Meysam %D 2022 %\ 01/01/2022 %V 8 %N 1 %P 33-41 %! Local subspace transitivity criterion %K Hypercyclic operators‎ %K ‎topologically transitive operators‎ %K ‎subspace hypercyclicity‎ %K ‎$J$-class operators %R 10.22034/kjm.2021.257086.2061 %X 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 maysatisfies in the local subspace transitivity criterion without being topological transitive. %U https://www.kjm-math.org/article_144157_0e1a07413ebf9a0676b3222933749466.pdf