Abstract

We characterize the commutative locally multiplicative convex (l.m.c.) algebras in terms of the spectral states. We also give a characterization of spectral states in terms of commutative semisimple l.m.c. algebras. Further, with the help of radicals of l.m.c. algebras we give a necessary and a sufficient condition for an algebra to be commutative modulo its radical.

Keywords: Spectral states, probability measure, l.m.c. algebra, commutative modulo.

MSC: 46J99, 46J15, 46K99

Pages:  15$-$19     

Volume  55 ,  Issue  1$-$2 ,  2003