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复Banach空间ℓp(Γ)(1 ≤ p < ∞)的Mazur-Ulam性质
The Mazur–Ulam Property for Complex Banach Space ℓp(Γ) (1 ≤ p < ∞)
1978年，Tingley提出著名的Tingley问题（等距延拓问题），受到许多学者的重视.遗憾的是到目前为止，即使对于二维Banach空间，这个问题仍是一个开问题.目前的研究主要集中在同类型或不同类型的经典Banach空间之间，并得到了肯定的回答.本文对复Banach空间ℓp（Γ）（1 ≤ p < ∞）与复Banach空间E之间的Tingley问题给出了肯定的回答，即复Banach空间ℓp（Γ）（1 ≤ p < ∞）满足Mazur-Ulam性质.
The Tingley's Probelm, which is named after the pioneering contribution of Tingley, is also known as the extension problem. It is nowadays a central topic for those researchers working on preservers. Up to the present, no negative counterexample is known and the general problem remains open even for two dimensional Banach spaces. The efforts gave rise to a wide list of positive answers to Tingley's problem for concrete classical Banach spaces and for some classes of Banach spaces. In this paper, we solved the Tingley's problem between the complex Banach spaces ℓp(Γ) (1 ≤ p < ∞) and complex Banach space E, i.e., we show that the complex Banach spaces ℓp(Γ) (1 ≤ p < ∞) satisfy the Mazur-Ulam property.
Tingley问题 / Mazur-Ulam性质 / 复Banach空间?p(Γ) {{custom_keyword}} /
Tingley's probelm / Mazur-Ulam property / complex Banach spaces ?p(Γ) {{custom_keyword}} /
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国家自然科学基金资助项目（11301384，11371201，11201337，11201338）
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