一类Banach空间中的分析性质及反例

Analysis Properties and Examples for a Class of Banach Space

中文关键词:  Banach空间  Schauder基  连续  可微  偏导数  坐标泛函

英文关键词:Banach space  Schauder base  continuous  differentiable  partial derivative.

中文摘要:

      本文对具有Schauder基的无穷维Banach空间上的映射定义偏导数,并讨论f的可徽性与偏导数存在并连续的关系;同时,本文还时论象所在空间为具有Schauder基的空间时,映射f与坐标映射f_i在可微性、连续性方面的关系.

英文摘要:

      We define partial derivative for a map f on Banach space with schauder base first, then discuss the relationship between differentiable property of f and existence and continuous of partial derivative of f. We also discuss the relationship between f and its coordinate functions f_i about differential and continuous properties when the image space is a Banach space with Schauder base.