Topological transitivity of the normalized maps induced by linear operators

Pabitra Narayan Mandal

https://orcid.org/0000-0002-8020-3371

India

University of Hyderabad

School of Mathematics and Statistics

Submitted: 2021-05-13

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Accepted: 2021-12-28

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Published: 2022-04-01

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

Copyright (c) 2022 Applied General Topology

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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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Keywords:

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

Supporting agencies:

NBHM-DAE (Government of India) Ref. No. 2/39(2)/2016/NBHM/R & D-II/11397

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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References:

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