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.