Generalized Toeplitz plus Hankel operators: kernel structure and defect numbers

Abstract

Generalized Toeplitz plus Hankel operators $T(a)+H_{\alpha }(b)$ generated by functions $a,b$ and a linear fractional Carleman shift $\alpha$ 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 $$a(t)a(\alpha (t))=b(t)b(\alpha (t)),t\in \mathbb{T},$$ the defect numbers of the operators $T(a)+H_{\alpha }(b)$ are established and an explicit description of the structure of the kernels and cokernels of the operators mentioned is given.

32 pages. arXiv admin note: text overlap with arXiv:1309.7574

References in corpus (1)

• Factorization of a class of Toeplitz + hankel operators and the A_p-condition