Linear Maps Between the Sequence Spaces $c$ and $c_0$

[摘要] This article aims to provide an elementary proof for the non­existence of a linear isometry from the Banach space $c$ to the Banach space $c_0$. This elementary proof was communicated to the first author by Prof. William B. Johnson. It is em­phasized that an isometry need not be onto. In order to place this result in an appropriate perspective, an elementary proof for the existence of a linear homeomorphism between the Ba­nach spaces $c$ and $c_0$ is also given. Also, the readers' attention is drawn to the fact that $c$ and $c_0$ are not nearly isometric to each other. In [1], Banach called two Banach spaces $X$ and $Y$ to be nearly isometric if the Banach-Mazur distance ($X, Y$) between them is 0. It should be noted that this is essentially a short exposi­tory article with a touch of history.

[学科分类] 社会科学、人文和艺术（综合）

[关键词] Sequence spaces;linear homeo­morphism;linear isometry.