Antinormal composition operators on \(l^2(\lambda)\). (English) Zbl 1465.47017

Kumar, Dilip; Chandra, Harish

Mat. Vesn. 68, No. 4, 259-266 (2016).

Summary: In this paper we characterize self-adjoint and normal composition operators on Poisson weighted sequence spaces \(ell^2(\lambda)\). 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 G. P. Tripathi and N. Lal [Tamkang J. Math. 39, No. 4, 347–352 (2008; Zbl 1192.47024)] to characterize antinormal composition operators on \(\ell^2(\lambda)\).

MSC:

47B33	Linear composition operators
47B15	Hermitian and normal operators (spectral measures, functional calculus, etc.)
47A53	(Semi-) Fredholm operators; index theories
47A05	General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47A58	Linear operator approximation theory
47B37	Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Keywords:

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

Citations:

Zbl 1192.47024