Abstract
Let θ be an inner function, let K θ = H 2 ⊖ θH 2, and let Sθ : Kθ → Sθ be defined by the formula Sθf = Pθzf, where f ∈ Kθ is the orthogonal projection of H2 onto Kθ. Consider the set A of all trace class operators L : Kθ → Kθ, L = ∑(·,un)vn, ∑∥un∥∥vn∥ < ∞ (un, vn ∈ Kθ), such that ∑ūn vn ∈ H 10 . It is shown that trace class commutators of the form XSθ − SθX (where X is a bounded linear operator on Kθ) are dense in A in the trace class norm. Bibliography: 2 titles.
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References
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M. Sh. Birman and M. Z. Solomyak, “Double operator integrals in a Hilbert space,” Integral Equations Operator Theory, 47, 131–168 (2003).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 54–61.
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Kapustin, V.V. Commutators in model spaces. J Math Sci 141, 1538–1542 (2007). https://doi.org/10.1007/s10958-007-0060-2
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DOI: https://doi.org/10.1007/s10958-007-0060-2