Local subspace transitivity criterion

Document Type : Original Article

Author

Meysam Asadipour

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

10.22034/kjm.2021.257086.2061

Abstract

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.

Keywords

Hypercyclic operators‎

‎topologically transitive operators‎

‎subspace hypercyclicity‎

‎$J$-class operators

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