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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.)

Citations:

Zbl 1192.47024
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