Jñānābha‎, Vol. 49 (1) (2019), 97-106

HYPERCYCLIC PAIR WHOSE COMPONENTS ARE DIRECT SUMS OF IDENTICAL HYPERCYCLIC OPERATORS

Neema Wilberth, Santosh Kumar and Marco Mpimbo

Department of Mathematics
College of Natural and Applied Sciences, University of Dar es Salaam, Tanzania
Email:neemawilberth@gmail.com, drsengar2002@gmail.com and
kmpimbo33@gmail.com
(Received : March 01, 2019 ; Revised: June 15, 2019)


Abstract

This paper provides an answer to the question raised by Feldman [15] which states that "If (T1, T2) is a hypercyclic pair, is (T1T1; T2T2) also a Hypercyclic Pair?" Some examples are provided to support the results.


2010 Mathematics Subject Classifications47A16, 47A15.
Keywords and phrasesHypercyclic pair, Hypercyclic criterion, Countably hypercyclic, Hypercyclic vector, Orbit, dense orbit.