The problem (set in [2]) of characterizing the subspaces of a commutative Banach algebra enjoying the property of multiplicative extension is solved under general assumptions and examples are given. Proofs will appear in another paper.
@article{RLINA_1976_8_61_5_333_0, author = {Sandro Levi}, title = {La propriet\`a di estensione moltiplicativa nelle algebre di Banach}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti}, volume = {60}, year = {1976}, pages = {333-336}, zbl = {0401.46028}, mrnumber = {0467318}, language = {it}, url = {http://dml.mathdoc.fr/item/RLINA_1976_8_61_5_333_0} }
Levi, Sandro. La proprietà di estensione moltiplicativa nelle algebre di Banach. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 60 (1976) pp. 333-336. http://gdmltest.u-ga.fr/item/RLINA_1976_8_61_5_333_0/
[1]
(1967) - Théories spectrales, Hermann, Paris.[2] Measure algebras on locally compact abelian groups: a case history in functional analysis, «Studia Math. (Ser. Specjalna) Zeszyt», 1, 41-52. | MR 147878 | Zbl 0116.08702
(1963) -[3] A class of multiplicative linear functionals on the measure algebra of a locally compact abelian group, «Illinois J. Math.», 4, 553-574. | MR 123198 | Zbl 0100.11803
e (1960) -[4] A problem of Hewitt on restrictions of multiplicative linear functionals, «Studia Math.», 25, 1-3. | MR 180834
(1964-65) -[5] The ideal space and Shilov boundary of a subalgebra of measures on a group, «J. Math. Anal. Appl.», 6, 266-276. | MR 149314 | Zbl 0124.07001
(1963) -[6] Banach algebra elements with independent powers, and theorems of Wiener-Pitt type. Function algebras (Proc. Internat. Sympos. on function algebras), Tulane Univ., 1965, pp. 186-197), Scott-Foresman, Chicago 111. | MR 198143
(1966) -