Vol. 68, No. 1, 1977

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Superalgebras of weak-Dirichlet algebras

Takahiko Nakazi

Vol. 68 (1977), No. 1, 197–207

Let A bs a weak-*Dirichlet algebra of L(m) and let Hx(m) denote the weak-*closure of A in L(m). Muhly showed that if H(m) is an integral domain, then H(m) is a maximal weak-*closed subalgebra of L(m). We show in this paper that if H(m) is not maximal as a weak-*closed subalgebra of L(m), there is no algebra which contains H(m) an is maximal among the proper weak-*closed subalgebras of L(m). Moreover, we investigate the weak-*closed superalgebras of A and we try to classify them. We show that there are two canonical weak-*closed superalgebras of A which play an important role in the problem of describing all the weak-*closed superalgebras of A.

Mathematical Subject Classification 2000
Primary: 46J10
Received: 6 April 1976
Published: 1 January 1977
Takahiko Nakazi
Hokusei Gakuen University
2-3-1, Ohyachi-Nishi
Atsubetsu-ku Sapporo 004-8631