International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 473-482
doi:10.1155/S0161171287000553
A new class of composition operators
S. Pattanayak
, C.K. Mohapatra
and A.K. Mishra
School of Mathematical Sciences, Sambalpur University, Jyoti Vihar 768019, India
Abstract
A new class of composition operators Pϕ:H2(T)→H2(T), with ϕ:T→D¯ is introduced. Sufficient conditions on ϕ for Pϕ to be bounded and Hilbert-Schmidt are obtained. Properties of Pϕ with ϕ(eit)=aeit+be−it for different values of the parameters a and b have been investigated. This paper concludes with a discussion on the compactness of Pϕ.