Talk:Banach–Stone theorem

It's a little misleading to say "...the Banach–Stone theorem allows one to recover a compact Hausdorff space from the algebra of scalars...". That is what Gelfand representation does if you assume the C*-structure: isomorphisms on the level of algebras gives homeomorphisms on spaces. The statement of Banach-Stone is stronger than that: isomorphism of Banach spaces gives homeomorphism and, on top of that, the given Banach space map is almost a Banach algebra map given by the induced homeomorphism. Mct mht (talk) 17:42, 4 May 2013 (UTC)