Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47888120220101Local subspace transitivity criterion334114415710.22034/kjm.2021.257086.2061ENMeysamAsadipourDepartment of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran0000-0001-6213-2074Journal Article20201112An operator $T$ on Banach space $X$ is called transitive,<br />if for every nonempty open subsets $U$,$V$ of $X$, there is a positive integer $n$, <br />such that $T^n (U) \cap V \neq\phi$. <br />In the present paper, local subspace transitivite operators are introduced.<br />We also provide nontrivial example and establish some basic properties of such operators.<br />Moreover the local subspace transitivity criterion is stated. Also, we show an operator may<br />satisfies in the local subspace transitivity criterion without being topological transitive.http://www.kjm-math.org/article_144157_0e1a07413ebf9a0676b3222933749466.pdf