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On the radical in hermitian LMC algebras. (English) Zbl 0628.46049

V. Pták [Manuscr. Math. 6, 245-290 (1972; Zbl 0229.46054)] proved that the radical (in the sense of Jacobson) of the Hermitian Banach star algebra is equal to the kernel of the spectral norm. The present paper will show that this is true also for every complete locally multiplicatively convex Hermitian star algebra.

MSC:

46H05 General theory of topological algebras

Citations:

Zbl 0229.46054

References:

[1] Bonsall F., Duncan J.: Complete Normed Algebras. Springer-Verlag (1973) · Zbl 0271.46039
[2] Michael E. A.: Locally Multiplicatively Convex Topological Algebras. Memoirs of AMS nb. 11 (1952) · Zbl 0047.35502
[3] Najmark M. A.: Normirovannyje koľča. Moskva (1968)
[4] Pták V.: Banach algebras with involution. Manuscripta math.6, Springer-Verlag (1972), 245-290 p. · Zbl 0229.46054 · doi:10.1007/BF01304613
[5] Štěrbová D.: Square roots and quasi-square roots in lmc algebras. AUPO (1980), 103-110.
[6] Štěrbová D.: On the fundamental inequality in lmc algebras. AUPO (1983), 47-52. · Zbl 0547.46029
[7] Štěrbová D.: Square roots of elements with an unbounded spectrum. AUPO (1984), to appear · Zbl 0603.46054
[8] Štěrbová D.: Generalization of the Shirali-Ford theorem in Hermitian lmc algebras. AUPO (1985), to appear · Zbl 0612.46047
[9] Želazko W.: Selected Topics in Topological Algebras. Lecture Notes Series N.31. (1971), Aarhus University. · Zbl 0221.46041
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