On spectrally convex ordinary algebras

A. Ouhmidou () and A. El Kinani ()
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A. Ouhmidou: Université Mohammed V de Rabat
A. El Kinani: Université Mohammed V de Rabat

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 349-354

Abstract: Abstract We prove that if A is an ordinary and advertibly complete $$l.m.c.a.\ $$ l . m . c . a . each element of which has a convex spectrum, then A modulo its Jacobson radical is isomorphic to $${\mathbb {C}}$$ C . We obtain the same conclusion for l.A.c.a and l.u.A-c.a. A purely algebraic version is also given. In the involutive case, the same conclusion, for an involutive ordinary Arens-Michael algebra, is obtained only under the convexity hypothesis on the spectrum of each normal element. Finally, if the algebra is additionally hermitian, it suffices to assume that the spectrum of each unitary element is convex.

Keywords: l.m.c.a.; Arens-Michael algebra; Ordinary algebra; Jacobson’s radical; Spectrum; Spectrally bounded algebra; Spectrally convex algebra; Advertibly complete algebra; Q-algebra; *-spectral Arens-Michael algebra; *-spectral hermitian Arens-Michael; 46H10; 13B02 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00006-x

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