Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 443-461

SOME RESULTS ON THE INVERTIBILITY OF TOEPLITZ PLUS HANKEL OPERATORS

Victor D. Didenko and Bernd Silbermann

Universiti Brunei Darussalam
Bandar Seri Begawan, BE1410 Brunei; diviol 'at' gmail.com

Technische Universität Chemnitz, Fakultät für Mathematik
09107 Chemnitz, Germany; silbermn 'at' mathematik.tu-chemnitz.de

Abstract. The paper deals with the invertibility of Toeplitz plus Hankel operators T(a) + H(b) acting on classical Hardy spaces on the unit circle T. It is supposed that the generating functions a and b satisfy the condition a(t)a(1/t) = b(t)b(1/t), t \in T. Special attention is paid to the case of piecewise continuous generating functions. In some cases the dimensions of null spaces of the operator T(a) + H(b) and its adjoint are described.

2010 Mathematics Subject Classification: Primary 47B35; Secondary 47B48.

Key words: Toeplitz plus Hankel operator, invertibility.

Reference to this article: V.D. Didenko and B. Silbermann: Some results on the invertibility of Toeplitz plus Hankel operators. Ann. Acad. Sci. Fenn. Math. 39 (2014), 443-461.

Full document as PDF file

doi:10.5186/aasfm.2014.3919