The commutants of relatively prime powers in Banach algebras
Author: Abdullah H. Al-Moajil
Journal: Proc. Amer. Math. Soc. 57 (1976), 243-249
MSC: Primary 46K05; Secondary 47B99
MathSciNet review: 0407612
Abstract: Let be a ring and belongs to the second commutant of for all integers . It is shown that in a prime ring if and only if has no nilpotent elements. The set is studied for some special -algebras. It is shown that the normal elements of a proper -algebra belong to . If is also prime then belongs to the second commutant of for some . The set is studied, where is the algebra of bounded operators on a Hilbert space . Necessary and sufficient conditions for some special types of operators to belong to are obtained.
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Keywords: Double commutant, proper involution, prime, algebraic operator
Article copyright: © Copyright 1976 American Mathematical Society