Vol. 37, No. 3, 1971

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Modular annihilator A-algebras

Pak-Ken Wong

Vol. 37 (1971), No. 3, 825–834

This paper is concerned with modular annihilator A-algebras. Let A be an A-algebra, B a maximal commutative -subalgebra of A and XB the carrier space of B. We show that the following statements are equivalent: (i) A is a modular annihilator algebra. (ii) Every XB is discrete. (iii) Every B is a modular annihilator algebra. (iv) The spectrum of every hermitian element of A has no nonzero limit points.

Let A be an A-algebra which is a dense two-sided ideal of a B-algebra A,A∗∗ the second conjugate space of A and πA the canonical embedding of A into A∗∗. We show that A is a modular annihilator algebra if and only if πA(A) is a two-sided ideal of A∗∗ (with the Arens product). This generalizes a recent result by B. J. Tomiuk and the author.

Mathematical Subject Classification 2000
Primary: 46K05
Received: 12 June 1970
Published: 1 June 1971
Pak-Ken Wong