Topological transitivity of  the normalized maps induced by linear operators

Pabitra Narayan Mandal

doi:10.4995/agt.2022.15613

Authors

Pabitra Narayan Mandal University of Hyderabad https://orcid.org/0000-0002-8020-3371

DOI:

https://doi.org/10.4995/agt.2022.15613

Keywords:

topological transitivity, supercyclicity, projective transformation, linear transformation, cone transitivity

Abstract

In this article, we provide a simple geometric proof of the following fact: The existence of transitive normalized maps induced by linear operators is possible only when the underlying space's real dimension is either 1 or 2 or infinity. A similar result holds for projective transformation as well.

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Author Biography

Pabitra Narayan Mandal, University of Hyderabad

School of Mathematics and Statistics

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