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

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.)

Zbl 1192.47024
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