Результаты исследований: Научные публикации в периодических изданиях › статья
Fredholmness and compactness of truncated Toeplitz and Hankel operators. / Bessonov, R.V.
в: Integral Equations and Operator Theory, 2014, стр. 1-17.Результаты исследований: Научные публикации в периодических изданиях › статья
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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 -
ID: 5758018