Hypercyclicity Criterion on Basic Elementary Operator
Kawira Esther *
Department of Physical Science, Chuka University, Kenya.
Denis N. King’ang’I
Department of Mathematics and Computer Science, University of Eldoret, Kenya.
Sammy W. Musundi
Department of Physical Science, Chuka University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Hypercyclicity criterion has been an important tool in the test of hypercyclicity of different operators. This tool has been used by different mathematicians to show that generalized derivations, left and right multiplication operators, operator algebra and backward shift operators are hypercyclic. In the current paper we show that a basic elementary operator satisfies the hypercyclicity Criterion.
Keywords: Hypercyclicity criterion, Rank one operator, Basic elementary operator