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Zapiski Nauchnykh Seminarov LOMI, 1985, Volume 141, Pages 56–71
(Mi znsl4166)
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The Adamyan–Arov–Krein theorem: Vectorial variant
S. R. Treil
Abstract:
One obtains the following description of the $s$–numbers of the vectorial Hankel operators $H_{\varphi}$, $\varphi\in L^{\infty}(E_1,E_2)$.
Theorem 1. {\it $s_n(H_{\varphi})=\inf\{\|H_{\varphi}-H_{\psi}\|:\operatorname{rank} H_{\psi}\le n\}$}.
The theorem generalizes the known Adamyan–Arov–Krein result and in the case $\min(\dim E_1,\dim E_2)<\infty$ has been proved by Ball and Helton. One obtains a constructive description of the Hankel operators of finite rank and one gives a formula for the rank of such an operator.
Citation:
S. R. Treil, “The Adamyan–Arov–Krein theorem: Vectorial variant”, Investigations on linear operators and function theory. Part XIV, Zap. Nauchn. Sem. LOMI, 141, "Nauka", Leningrad. Otdel., Leningrad, 1985, 56–71; J. Soviet Math., 37:5 (1987), 1297–1306
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https://www.mathnet.ru/eng/znsl4166 https://www.mathnet.ru/eng/znsl/v141/p56
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Abstract page: | 175 | Full-text PDF : | 64 |
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