Abstract

In this paper, we characterize self-adjoint and normal composition operators on Poisson weighted sequence spaces $l^{2}(\lambda)$. However, the main purpose of this paper is to determine explicit conditions on inducing map under which a composition operator admits a best normal approximation. We extend results of Tripathi and Lal [Antinormal composition operators on $l^2$, Tamkang J. Math. 39 (2008), 347-352] to characterize antinormal composition operators on $l^{2}(\lambda)$.

Keywords: composition operator; normal operator; antinormal operator; Fredholm operator; self-adjoint operator; Poisson weighted sequence spaces.

MSC: 47B33, 47A05, 47A58, 47B37

Pages:  259$-$266     

Volume  68 ,  Issue  4 ,  2016