B(s, 2) Algebras
نویسنده
چکیده
1. Closed ideals. (1.1) Definition. Let 5 be an arbitrary set, and 2 a Boolean ring of subsets of 5. The algebra B(S, 2) consists of all uniform limits of finite linear combinations of characteristic functions of sets in 2. The norm in B(S, 2) is given by the formula ||/|| =SupseS \f(s) | • This definition is slightly more general than that given in [l ] where 2 is required to be a field of sets (Boolean ring with identity = Boolean algebra). (1.2) Definition. A simple function in B(S, 2) is a finite linear combination of characteristic functions of sets in 2.
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