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タイトル: | Surjective isometries on an algebra of analytic functions with $C^n$-boundary values (Research on preserver problems on Banach algebras and related topics) |
著者: | ENAMI, Yuta MIURA, Takeshi |
キーワード: | 46B04 46J15 extreme point function space surjective isometry |
発行日: | Jul-2023 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B93 |
開始ページ: | 83 |
終了ページ: | 107 |
抄録: | Let 𝔻, 𝔻⁻ and 𝕋 be the open unit disk, closed unit disk and unit circle in ℂ. Let $A^n$(𝔻⁻) denote the algebra of all continuous functions f on 𝔻⁻ which are analytic in 𝔻 and whose restrictions f|𝕋 to T are of class $C^n$. For each f ∈ $A^n$(𝔻⁻), the k-th derivative of f|𝕋 as a function on 𝕋 is denoted by D^k(f). We characterize surjective, not necessarily linear, isometries on $A^n$(𝔻⁻) with respect to the norm ∥f∥𝔻⁻ + Σ[n][k=1]∥$D^k$(f)∥𝕋/k!, where ∥ · ∥𝔻⁻ and ∥ · ∥𝕋 are the supremum norms on 𝔻⁻ and 𝕋, respectively. |
著作権等: | © 2023 by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. All rights reserved. Printed in Japan. |
URI: | http://hdl.handle.net/2433/284872 |
出現コレクション: | B93 Research on preserver problems on Banach algebras and related topics |
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