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Essentially commuting Hankel and Toeplitz operators. (English) Zbl 1036.47016
Let $$T_f$$ and $$H_g$$ denote Toeplitz and Hankel operators in the Hardy space $$H^2$$ which is a subspace of $$L^2 (\partial D, d\sigma),$$ where $$d\sigma$$ is the normalized Lebesgue measure on the unit circle $$\partial D$$. The authors study the question when the commutator $$[H_g, T_f]=H_gT_f-T_fH_g$$ of Hankel and Toeplitz operators is compact. They find some criteria for $$[H_g, T_f]$$ to be compact.

MSC:
 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 46J15 Banach algebras of differentiable or analytic functions, $$H^p$$-spaces
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References:
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