# Where was the Banach-Mazur Theorem originally published?

I would like to cite the original source for the Banach-Mazur Theorem that the space $\mathcal{C}([0,1])$ of continuous functions on the unit interval is universal for separable Banach spaces, i.e., that for every separable Banach space $X$ there is an isometric embedding $i\colon X\to\mathcal{C}([0,1])$. In the books on functional analysis I have there is no reference to the original proof of this result.

In short my question is: where was the Banach-Mazur Theorem published originally?

## 1 Answer

Kleiber and Pervin (1969) cite Banach's monograph Théorie des Opérations Linéaires (1932) for the "classical theorem of Banach and Mazur". Here is a scanned copy of the original edition (in French) on Banach's home page. There is an English translation available from Dover.

• For easier navigation, this is Theorem 9 in Chapter XI. It does not seem to correspond to any earlier published joint work by Banach and Mazur. They did publish several papers on the problem of a linear normed space being isomorphic to a subspace of another one, e.g. Zur Théorie der linearen Dimension, Studia Mathematica 4 (1933), 100-112, available from Banach's homepage, kielich.amu.edu.pl/Stefan_Banach/oeuvres.html May 6 '16 at 1:29