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arXiv · 1407.3466

Fredholmness and compactness of truncated Toeplitz and Hankel operators

R. V. Bessonov
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Abstract

We prove the spectral mapping theorem $\sigma_e(A_\phi) = \phi(\sigma_e(A_z))$ for the Fredholm spectrum of a truncated Toeplitz operator $A_\phi$ with symbol $\phi$ in the Sarason algebra $C+H^\infty$ acting on a coinvariant subspace $K_\theta$ of the Hardy space $H^2$. Our second result says that a truncated Hankel operator on the subspace $K_\theta$ generated by a one-component inner function $\theta$ is compact if and only if it has a continuous symbol. We also suppose a description of truncated Toeplitz and Hankel operators in Schatten classes $S^p$.

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R. V. Bessonov. 2014-07-13. Fredholmness and compactness of truncated Toeplitz and Hankel operators. https://doi.org/10.1007/s00020-014-2177-2

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