Continuité des Caractères Dans les Algèbres de Fréchet à Bases
Canadian mathematical bulletin, Tome 31 (1988) no. 2, pp. 168-174
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In [1] and [2] T. Husain and J. Liang show the following results: RI. Every character on a Fréchet algebra with a Schauder basis (xi )i≧1 such that: (1) XiXj = XjXi = Xj if i ≦j, (2) Pi (Xi ) ≠ 0 and Pi (xi+1 ) = 0 (where (pi)i≧1is a denumerable family of semi-norms defining the topology of the algebra) is continuous. R2. Every character on a Fréchet algebra with orthogonal and unconditional Schauder basis is continuous. The proofs of these last results are very long and introduce complex calculation without aid of spectral theory of locally ra-convex algebras. We give here short proofs of these results with aid of a characterization of elements of the spectrum in locally m-convex algebras with values of characters.
Akkar, M.; Azhari, M. El; Oudadess, M. Continuité des Caractères Dans les Algèbres de Fréchet à Bases. Canadian mathematical bulletin, Tome 31 (1988) no. 2, pp. 168-174. doi: 10.4153/CMB-1988-025-9
@article{10_4153_CMB_1988_025_9,
author = {Akkar, M. and Azhari, M. El and Oudadess, M.},
title = {Continuit\'e des {Caract\`eres} {Dans} les {Alg\`ebres} de {Fr\'echet} \`a {Bases}},
journal = {Canadian mathematical bulletin},
pages = {168--174},
year = {1988},
volume = {31},
number = {2},
doi = {10.4153/CMB-1988-025-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-025-9/}
}
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[1] 1. Husain, T. and Liang, J., Multiplicative functionals on Fréchet algebras with bases, Can. J. Math. Vol XXIX n° 2 (1977), pp. 270–276. Google Scholar
[2] 2. Husain, T. and Liang, J., Continuity of multiplicative linear functionals on Fréchet algebras with bases, Bull. Soc. Roy. Se Liège 46 (1977), pp. 8–11. Google Scholar
[3] 3. Michaël, E. A., Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc. 11 (1952). Google Scholar
[4] 4. Schaefer, H. H., Topological vector spaces (MacMillan New York 1964). Google Scholar
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