A necessary and sufficient condition is given for a*-algebra with identity to have a unique maximal C*-seminorm. This generalizes the result, due to Bonsall, that a Banach *-algebra with identity has such a*-seminorm.
@article{bwmeta1.element.bwnjournal-article-smv118i1p19bwm,
author = {Bertram Yood},
title = {C*-seminorms},
journal = {Studia Mathematica},
volume = {119},
year = {1996},
pages = {19-26},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv118i1p19bwm}
}
Yood, Bertram. C*-seminorms. Studia Mathematica, Tome 119 (1996) pp. 19-26. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i1p19bwm/
[00000] [1] F. F. Bonsall, A survey of Banach algebra theory, Bull. London Math. Soc. 2 (1970), 257-274. | Zbl 0207.44201
[00001] [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973. | Zbl 0271.46039
[00002] [3] I. Gelfand and M. Naimark, Rings with involution and their representations, Izv. Akad. Nauk SSSR Ser. Mat. 12 (1948), 445-480 (in Russian).
[00003] [4] I. Kaplansky, Topological algebras, Dept. of Math., Univ. of Chicago, 1952 (mimeographed notes). | Zbl 0048.26902
[00004] [5] I. Kaplansky, Topological Algebras, Notas Mat. 16, Rio de Janeiro, 1959.
[00005] [6] M. Naimark, Normed Rings, Noordhoff, Groningen, 1960.
[00006] [7] V. Pták, Banach algebras with involution, Manuscripta Math. 6 (1972), 245-290. | Zbl 0229.46054
[00007] [8] C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, Princeton, 1960.
[00008] [9] B. Yood, Homomorphisms on normed algebras, Pacific J. Math. 8 (1958), 373-381. | Zbl 0084.33601
[00009] [10] B. Yood, Faithful *-representations of normed algebras, ibid. 10 (1960), 345-363.