TY - JOUR

T1 - Fredholmness and compactness of truncated Toeplitz and Hankel operators

AU - Bessonov, R.V.

PY - 2014

Y1 - 2014

N2 - 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 $S^p$.

AB - 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 $S^p$.

KW - Truncated Toeplitz operators

KW - truncated Hankel operators

KW - spectral mapping theorem

KW - Schatten ideal.

U2 - 10.1007/s00020-014-2177-2

DO - 10.1007/s00020-014-2177-2

M3 - Article

SP - 1

EP - 17

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

ER -