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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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