Geodesic
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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DOI

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.
DOI : 10.4153/CMB-1988-025-9
Mots-clés : 46H15 
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
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     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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