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?


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.

  • 2
    $\begingroup$ 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 $\endgroup$ – Margaret Friedland May 6 '16 at 1:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.