Abstract
The classical Adamjan-Arov-Krein theorem relating the singular numbers of Hankel operators to best approximations of their symbols has an abstract version for unitary representations of the discrete group IIn, n ≥ 1 [CS4]. Here we obtain similar results for the regular representations of ℝn, n ≥ 1, and the symplectic spaces. This is based on lifting theorems and on the characterizations of the generators and cogenerators of semiunitary semigroups. In particular, it is shown that all compact Hankel operators in ℝn, n ≥ 1, and in the symplectic spaces are zero.
Author partially supported by NSF(USA) grant DMS89-11717.
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Dedicated to our friend Harold Widom, in his 60th birthday.
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© 1994 Birkhäuser Verlag
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Cotlar, M., Sadosky, C. (1994). The Adamjan-Arov-Krein Theorem in General and Regular Representations of R2 and the Symplectic Plane. In: Basor, E.L., Gohberg, I. (eds) Toeplitz Operators and Related Topics. Operator Theory Advances and Applications, vol 71. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8543-0_6
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DOI: https://doi.org/10.1007/978-3-0348-8543-0_6
Publisher Name: Birkhäuser, Basel
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