On Subspace-ergodic Operators


  • Mansooreh Moosapoor Department of Mathematics, Farhangian University, Tarbiat Moallem Ave, Tehran 1998963341.




ergodic operators, mixing operators, subspace-ergodic operators, subspace-mixing operators.


In this paper, we define subspace-ergodic operators and give examples of these operators. We show that by any given separable infinite-dimensional Banach space, subspace-ergodic operators can be constructed. We demonstrate that an invertible operator T is subspace-ergodic if and onlyif T-1 is subspace-ergodic. We prove that the direct sum of two subspace-ergodic operators is subspace-ergodic and if the direct sum of two operators is subspace-ergodic, then each of them is subspace-ergodic. Also, we investigate relations between subspace-ergodic and subspace-mixing operators. For example, we show that if T is subspace-mixing and invertible, then Tn and T-n are subspace-ergodic for n??.


Grosse-Erdmann, K.G. & Peris Manguillot, A., Linear Chaos, Springer-Verlag London Ltd., 2011.

Bes, J., Menet, Q., Peris, A., & Puig, Y., Strong Transitivity Properties for Operators, J. Differ. Equ., 266, pp. 1313-1337, 2019.

Conejero, J.A. & Peris, A., Linear Transitivity, Top. Appl., 153, pp. 767-773, 2005.

Costakis, G. & Sambarino, M., Topologically Mixing Hypercyclic Operators , Proc. Amer. Math. Soc., 132, pp. 385-389, 2003.

Grivaux, S., Mixing Operators and the Bounded Steps Problem, J. Operat. Theor., 6, pp. 51-58, 2012.

Grosse-Erdmann, K.G. & Peris, A., Weakly Mixing Operators on Topological Vector Spaces, RACSAM., 104, pp. 413-426, 2010.

Madore, B.F. & Martinez-Avendano, R.A., Subspace Hypercyclicity, J. Math. Anal. Appl., 373, pp. 502-511, 2011.

Rezaei, H., Notes on Subspace-hypercyclic Operators, J. Math. Anal. Appl., 397(1), pp. 428-433, 2013.

Martinez-Avendano, R.A. & Zatarain-Vera, O., Subspace-hypercyclicity for Toeplitz Operators, J. Math. Anal. Appl., 422(1), pp. 60-68, 2015.

Bamerni, N., Kadets. V. & Kilicman, A., Hypercyclic Operators Are Subspace-hypercyclic, J. Math. Anal. Appl., 435(2), pp. 1812-1815, 2016.

Zhang, L. & Zhou, Z.H., Notes About Subspace-supercyclic Operators, Ann. Funct. Anal., 6(2), pp. 60-68, 2015.

Talebi, S. & Moosapoor, M., Subspace-chaotic and Subspace-weakly Mixing Operators, Int. J. Pure. Appl. Math., 78, pp. 879-885, 2012.

Moosapoor, M., Subspace-mixing Operators and Subspace-weakly Mixing Operators, Pioneer Journal of Mathematics and Mathematical Sciences, 6, pp. 51-58, 2012.

Bamerni, N. & Kilicman, A., On the Direct Sum of Two Bounded Linear Operators and Subspace-hypercyclicity, General Letters in Mathematics, 8(1), pp. 1-7, 2020.