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We characterize Gelfand-continuous functions from a Tychonoff space $X$ into an Arens-Michael algebra $A$. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras $A$ and locally compact spaces $X$ for which all these algebras differ from each other.
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참고문헌 (13)
참고문헌 신청
G. R. Allan / 1965 / A spectral theory for locally convex algebras / Proc. London Math. Soc. (3) 15:399~421
R. Arens / 1952 / A generalization of normed rings / Pacic J. Math 2:455~471
F. F. Bonsall / 1973 / Complete Normed Algebras / Springer-Verlag
R. C. Buck / 1958 / Bounded continuous functions on a locally compact space / Michigan Math. J 5:95~104
H. El Adlouni / 2000 / Groupe des inversibles et rayon spectral dans les algebres topologiques / Rend. Circ. Mat. Palermo (2) 49(3):527~539
R. Arens / 1952 / A generalization of normed rings / Pacic J. Math 2:455~471
F. F. Bonsall / 1973 / Complete Normed Algebras / Springer-Verlag
R. C. Buck / 1958 / Bounded continuous functions on a locally compact space / Michigan Math. J 5:95~104
H. El Adlouni / 2000 / Groupe des inversibles et rayon spectral dans les algebres topologiques / Rend. Circ. Mat. Palermo (2) 49(3):527~539
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