Some examples of composition operators and their approximation numbers on the Hardy space of the bi-disk
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چکیده
We give examples of composition operators CΦ on H(D) showing that the condition ‖Φ‖∞ = 1 is not sufficient for their approximation numbers an(CΦ) to satisfy limn→∞[an(CΦ)] √ n = 1, contrary to the 1-dimensional case. We also give a situation where this implication holds. We make a link with the Monge-Ampère capacity of the image of Φ. Key-words : approximation numbers; Bergman space; bidisk; composition operator; Green capacity; Hardy space; Monge-Ampère capacity; weighted composition operator. MSC 2010 numbers – Primary: 47B33 – Secondary: 30H10 – 30H20 – 31B15 – 32A35 – 32U20 – 41A35 – 46B28
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