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大学・研究所にある論文を検索できる 「Surjective isometries on an algebra of analytic functions with $C^n$-boundary values (Research on preserver problems on Banach algebras and related topics)」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

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Surjective isometries on an algebra of analytic functions with $C^n$-boundary values (Research on preserver problems on Banach algebras and related topics)

ENAMI, Yuta MIURA, Takeshi 京都大学

2023.07

概要

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.

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