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arXiv · 1501.04271

Generalized Toeplitz plus Hankel operators: kernel structure and defect numbers

Victor D. Didenko·Bernd Silbermann
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Abstract

Generalized Toeplitz plus Hankel operators $T(a)+H_α(b)$ generated by functions $a,b$ and a linear fractional Carleman shift $α$ changing the orientation of the unit circle $\mathbb{T}$ are considered on the Hardy spaces $H^p(\mathbb{T})$, $1<p<\infty$. If the functions $a,b\in L^\infty(\mathbb{T})$ and satisfy the condition $$ a(t) a(α(t))=b(t) b(α(t)),\quad t\in \mathbb{T}, $$ the defect numbers of the operators $T(a)+H_α(b)$ are established and an explicit description of the structure of the kernels and cokernels of the operators mentioned is given.

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Victor D. Didenko, Bernd Silbermann. 2015-01-18. Generalized Toeplitz plus Hankel operators: kernel structure and defect numbers. https://arxiv.org/abs/1501.04271

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