@article {MATHEDUC.02074199,
author = {Kulkarni, S.H.},
title = {A very simple and elementary proof of a theorem of Ingelstam.},
year = {2004},
journal = {American Mathematical Monthly},
volume = {111},
number = {1},
issn = {0002-9890},
pages = {54-58},
publisher = {Mathematical Association of America (MAA), Washington, DC},
doi = {10.2307/4145018},
abstract = {The theorem in question states that a unital Banach algebra over the field $\Bbb R$ whose underlying Banach space is a (real) Hilbert space is isomorphic to one of the algebras $\Bbb R$, $\Bbb C$ or $\Bbb H$ (=~quaternions), cf.\ [{\it I.~Ingelstam}, Math. Scand. 11, 22--32 (1962; Zbl 0122.35003)]. The paper under review certainly lives up to its title since no Banach algebra theory and barely any Hilbert space theory is used; incidentally, completeness turns out to be inessential for the theorem. The only criticism I have is that the author's reasoning for Fact~1 only works if the set $S$ is assumed orthonormal and that the name Schwarz in Cauchy-Schwarz inequality is misspelt two thirds of the time.},
reviewer = {Dirk Werner (Berlin)},
msc2010 = {I95xx},
identifier = {2007f.00384},
}