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 (T1⊕T1; T2⊕T2) also a Hypercyclic Pair?" Some examples are provided to support the results.
2010 Mathematics Subject Classifications: 47A16, 47A15.
Keywords and phrases: Hypercyclic pair, Hypercyclic criterion, Countably hypercyclic, Hypercyclic vector, Orbit, dense orbit.