Families of Homomorphisms in Non-commutative Gelfand Theory: Comparisons and Examples
In non-commutative Gelfand theory, families of Banach algebra homomorphisms, and particularly families of matrix representations, play an important role.D epending on the properties imposed on them, they are called sufficient, weakly sufficient, partially weakly sufficient, radical-separating or separating.I n this paper these families are compared with one another. Conditions are given under which the defining properties amount to the same. Where applicable, examples are presented to show that they are genuinely different.
KeywordsBanach algebra homomorphism matrix representation sufficient family weakly sufficient family partially weakly sufficient family radicalseparating family separating family polynomial identity algebra spectral regularity
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