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Journal of Operator Theory

Volume 78, Issue 2, Fall 2017  pp. 293-307.

Invertibility and inverses of Toeplitz plus Hankel operators

Authors:  Victor Didenko (1) and Bernd Silbermann (2)
Author institution:(1) Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
(2) Fakult{\"a}t f\"ur Mathematik, Technische Universit{\"a}t Chemnitz, 09107, Chemnitz, Germany

Summary: Necessary conditions for the invertibility of Toeplitz plus Hankel operators $T(a)+H(b)$ with generating functions $a,b\in L_\infty(\mathbb T)$ satisfying the relation $a(t)a(1/t)=b(t)b(1/t)$, $t\in\mathbb T$ are obtained. In addition, sufficient conditions for the invertibility of such operators are also provided and efficient representations for the corresponding inverses are derived.

Keywords: Toeplitz plus Hankel operators, matching functions, invertibility, inverses

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