Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2022), 345 -- 356

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ON SPECTRALLY FINITE FRÉCHET ALGEBRAS

D. El Boukasmi and A. El Kinani

Abstract. We show that a spectrally finite Fréchet algebra is finite-dimensional modulo its Jacobson radical. If moreover, the algebra has no nonzero quasi-nilpotent elements, then it is\ semi-simple and commutative and so isomorphic to ℂn for an integer n∈ ℕ.

2020 Mathematics Subject Classification: 46H05, 46H20.
Keywords: Spectrally finite algebra, Jacobson radical, Algebraic algebra, Finite dimensional algebra, Semi-simple algebra, Q-algebra, l.m.c.a., Fréchet algebra, Baire space.

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D.El Boukasmi
Université Mohammed V de Rabat, E.N.S de Rabat, B. P. 5118, 10105,
Rabat, Maroc.
email: ddriss6@gmail.com


A.El Kinani
Université Mohammed V de Rabat, E.N.S de Rabat, B. P. 5118, 10105,
Rabat, Maroc.
e-mail: abdellah.elkinani@um5.ac.ma


http://www.utgjiu.ro/math/sma