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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

BOUKASMI, D. El  and  KINANI, A. El. Spectral operation in locally convex algebras. Proyecciones (Antofagasta) [online]. 2022, vol.41, n.3, pp.683-695. ISSN 0716-0917.  http://dx.doi.org/10.22199/issn.0717-6279-4548.

We show that if A is a spectrally bounded algebra, then all functions operate spectrally on A if and only if SpAx is finite for every x ∈ A. We also prove that if A is a commutative Q-l.m.c.a, then all functions operate spectrally on A if and only if A/RadA is algebraic. Furthermore, if A is a semi-simple commutative Q-l.m.c.a. which is a Baire space, all functions operate spectrally on A if and only if it is isomorphic to C n for some n ∈ N. A structure result concerning semi-simple commutative complete m-convex algebras of countable dimension is also given.

Keywords : Spectrally bounded algebra; Q-algebra; l.m.c.a.; algebraic algebra; Baire space; Fourier-Gelfand transform; algebra of countable Hamel basis; operate function; function operate spectrally.

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